This book provides an analysis of the construction, diagnosis (as chaotic) and evaluation of models in chaos theory. It contains a detailed look at the interaction of the different models used in chaos theory and analyses how these models influence the way chaos is defined. Furthermore, the book discusses the conditions for the occurrence of chaos and the detection of chaos in nature.

This book reports recent landmark developments and the state of the art in NDS science in psychological theory and research.

This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as "chaos theory," surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples-both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude (...) with some reflections on the nature of arguments that seek to establish intellectual authority or epistemic merit by analogical reasoning. (shrink)

This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as “chaos theory,” surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples—both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude (...) with some reflections on the nature of arguments that seek to establish intellectual authority or epistemic merit by analogical reasoning. (shrink)

This book provides an analysis of the construction, diagnosis (as chaotic) and evaluation of models in chaos theory. It contains a detailed look at the interaction of the different models used in chaos theory and analyses how these models influence the way chaos is defined. Furthermore, the book discusses the conditions for the occurrence of chaos and the detection of chaos in nature.

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be (...) the most useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Chaos and Clinical TheoryDouglas W. Heinrichs (bio)In considering the specific issues raised by these three very thoughtful commentaries, it is helpful to reflect on the status of a theory or model for a specifically clinical discipline—what is it trying to accomplish and how might it proceed to do so? Kellert (2005) sees my proposal in terms of "borrowed knowledge"—the metaphorical application of a theory established in one field (...) of inquiry to another field—and views my application of chaos theory as a "nonliteral use of knowledge from the natural sciences" (p. 239). He likens it to attempts to explore consequences of relativity theory or quantum mechanics for areas other than those for which they were developed. He notes the rhetorical functions—including appeal to the disciplinary prestige of natural science—of such metaphorical borrowings.Although clearly there are significant metaphorical aspects at work here, there are at least two factors that distinguish this model from, say, the metaphorical application of quantum mechanics to a field other than subatomic physics. First, quantum mechanics purports to say something specific about the behavior of the subatomic world. Its development is wed to that specific content area. On the other hand, nonlinear dynamics, including chaos theory, is a formal mathematical model intending to characterize the behavior of any system of elements that possess certain formal relational properties. It does not start out as field or discipline specific. In fact it is not uniquely tied to the natural sciences at all, beyond the fact that it may be easier to obtain the sort of detailed repeated measures needed to demonstrate chaotic behavior in physical systems. So it is not just a question of whether chaos theory is a useful intuitive device for thinking freshly about clinical psychiatry. Rather, it is the quite literal and nonmetaphorical question as to whether some of the observable aspects of persons that are relevant to their psychiatric care behave chaotically, and if so what are the implications.Now it is quite true that direct, mathematically rigorous demonstrations of chaos in clinically relevant data sets is currently limited. In fact, one hoped for consequence of presenting this model is to encourage just such studies, and I suggest several promising directions for doing so. However, there are good reasons for thinking the presence of such chaotic behavior to be likely, and this relates to the notion of a clinical theory.One of the consequences of what Globus (2005) calls "triumphalist biological psychiatry" (p. 229) is the frequent assumption that the model or paradigm of psychiatry—an applied clinical practice, a techne—is synonymous with the paradigm of neuroscience—a basic science or episteme. This is clearly not so for many reasons, including the fact that the former has to incorporate the comprehensive treatment of discrete individuals in a way that the latter does not. Yet the respective theories are related more than metaphorically. [End Page 243] The paradigms of neuroscience and those of other relevant basic sciences, such as psychology, substantially inform the clinical paradigm and the clinical model must be at least compatible with those of the relevant basic sciences. Thus, it is reasonable to assume that if chaotic processes are demonstrable in the nervous system, for which significant evidence already exists, there is good reason to expect them to be reflected in clinically relevant domains. The clinical paradigm should make room for it and its consequences, rather than thinking within an outmoded neuroscience model that makes no room for the implications of nonlinear dynamics. And when this generates a picture more compatible than the old model with our usual sense of what it is to be human, the odds that we are on to something is further enhanced. Of course until such time that enough clinical research based on this model is completed, considerable speculation—indeed aided by metaphorical devices—is involved in generating a concrete sense of how the model would be applied to specific clinical problems, such as the treatment of depressed persons.One clear task of the clinical paradigm is the methodologic integration of interventions growing out of different informing basic sciences. Because chaotic modeling can be applied across various content domains and... (shrink)

The main purpose of this book is to introduce a broader audience to emergence by illustrating how discoveries in the physical sciences have informed the ways we think about it. In a nutshell, emergence asserts that non-reductive behavior arises at higher levels of organization and complexity. As physicist Philip Anderson put it, "more is different." Along the text's conversational tour through the terrain of quantum physics, phase transitions, nonlinear and statistical physics, networks and complexity, the author highlights the various (...) philosophical nuances that arise in encounters with emergence. The final part of the book zooms out to reflect on some larger lessons that emergence affords us. One of those larger lessons is the realization that the great diversity of theories and models, and the great variety of independent explanatory frameworks, will always be with us in the sciences and beyond. There is no "Theory of Everything" just around the corner waiting to be discovered. One of the main benefits of this book is that it will make a number of exciting scientific concepts that are not normally covered at this level accessible to a broader audience. The overall presentation, including the use of examples, analogies, metaphors, and biographical interludes, is geared for the educated non-specialist. (shrink)

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link (...) these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws. (shrink)

We present the historical development of Nonlinear Dynamical Astronomy with emphasis on the “third integral” and its applications. The new era started with the use of computers, and of formal analytical developments in the spirit of Poincaré. Most dynamical systems were found to contain both ordered and chaotic orbits. The transition from order to chaos is discussed. Recent developments refer to the dynamical spectra, integrals of notion in self-consistent models, systems of 3 or more degrees of freedom, (...) chaos in relativity and cosmology, and chaos in quandum mechanics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 239-242 [Access article in PDF] The Uses of Borrowed Knowledge: Chaos Theory and Antidepressants Stephen H. Kellert Keywords chaos, metaphor, rhetoric, values Ever since the popularization of chaos the-ory in the 1980s, there has been an explo-sion of interest in work in nonlinear dynamics generally and the study of strange attractors in particular. From law to economics to (...) theology, researchers in the social sciences and the humanities have sought to make use of the concepts, methods, and results of chaos theory. Previous generations have seen similar attempts to explore the consequences of relativity theory or quantum mechanics for their own areas of inquiry. In examining the implications of chaos for the treatment of mental illness, Douglas Heinrichs provides an example of this phenomenon, which I call "borrowed knowledge." Lacking expertise in the areas of psychotherapy or psychopharmacology, I view his suggestions as a case study in the ways that knowledge gets used across disciplinary boundaries. In these remarks, I examine some of the different functions that borrowed knowledge can serve in order to argue that although cross-disciplinary borrowing can be a fruitful source of new insights, it is not without its dangers. I look at the persuasive function that borrowed knowledge can serve in making one's ideas plausible candidates for further exploration, as well as in motivating methodological change. I look at the conceptual work performed by metaphors, paying special attention to the question of how we can judge whether or not a nonliteral use of knowledge from the natural sciences is fruitful. And finally, I look at the ways in which borrowed knowledge can be used to address evaluative questions—in this case, questions about autonomy and appropriate therapeutic practice. I do not mean for these various functions to be thought of as exclusive categories. Instead, they overlap, interact, and combine in various ways. Rhetorical Functions, Disciplinary Prestige, and Methodologic Change In examining the persuasive uses of chaos theory, I should make it clear that by "persuasive" I do not mean illegitimate or deceptive. When Heinrichs points out that what he calls the traditional model of brain function is used to [End Page 239] present and explain the use of antidepressants (ADs) to clinicians and the general public, it becomes clear that he believes an alternative model can be useful for explicating and justifying the use of ADs for clinicians and patients. This descriptive function of the metaphorical appeal to a chaotic "attractor landscape" shows up where Heinrichs discusses the use of the chaotic model for patient education and the "rationale for pharmacotherapy," giving patients "appropriate expectations."But the rhetorical functions of chaos theory also come into play with audiences other than patients; they apply to the audience for the scholarly article itself, perhaps attracting attention because of the novelty or promise of a new field of research, but also harnessing the considerable disciplinary prestige that the natural sciences wield in our culture. All of these functions are useful in directing attention to the author's suggestions for further research, especially where he suggests that it would provide the clinician with guidance in working with an individual patient. Here I take it that Heinrichs has made fruitful use of the work of Thelen and others on the variability of individual developmental trajectories. This proposal for methodological change suggests that focusing on the dynamics of system and its evolution through time may be important in addition to focusing on equilibrium states. The disciplinary prestige of the natural sciences can provide a valuable and legitimate resource for the persuasive task of encouraging one's colleagues to explore a new methodological approach.A further rhetorical use is found in the appeal to the unpredictability of chaotic systems to account for the variability of results in the application of ADs. We see this where Heinrichs says, "a meaningful science of persons is possible even in the face of their ultimate unpredictability" (2005, 221). The disciplinary prestige of the natural sciences, which in studying chaotic systems are able to achieve genuinely "scientific" status without being able... (shrink)

With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and (...) discuss new perspectives on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory. (shrink)

Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities (...) of nonlinear systems.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 235-237 [Access article in PDF] Determined by Chaos: The Nonlinear Dynamics of Free Will Jessica Wahman Keywords free will, chaos theory, determinism, materialism In "antidepressants and the Chaotic Brain: Implications for the Respectful Treatment of Selves," Douglas Heinrichs provides an intriguing justification of individuated and longer term therapy for depressive clients. He does not reject medication as a therapeutic (...) strategy, nor does he question the materialist basis of the traditional medical model. Rather, he offers a physically deterministic account of depression that is at the same time compatible with a sense of human agency and individuality. Heinrichs suggests that human physiology and its psychiatric disorders are better accounted for by the nonlinear dynamics of chaos theory than by the traditional account of neurotransmitter production and reuptake. Because the latter, microscopic, explanation suggests a direct cause-and-effect relationship between synaptic activity and subjective affect, it cannot account for the wide variation of responses to the same medications, nor can it satisfy the client's fears that her drug-induced well-being is not fully hers to control. Chaos theory, he asserts, can provide a better explanation by treating the human organism as a complex holistic system whose patterns resemble a topographical map of probability more than they do a unidirectional vector model of cause to effect. Like the weather, human affect and behavior are physically determined but difficult to predict, and so careful attention to both the individual history of the client and the uniqueness of responses to medication are a necessary part of any successful therapeutic program.Connected to this theory of nonlinear physiology is Heinrichs's account of autonomy and agency under this rubric. He notes that a psychology based on chaos theory is not only compatible with the notion of free will, it can better explain why the successful use of medication actually increases freedom and autonomy instead of limiting it. It is here that I wish to focus my comments, because his interpretation of free will may give us, to borrow a phrase from Daniel Dennett, a "variet[y] of free will worth wanting" (1984, title page). Free will, in this case, is not a metaphysical ability to act above and beyond our material causes, but is instead a property of the material system itself, namely when that system feels itself capable of greater psychic mobility around the topographical map of probabilistic patterns.According to this model, our ability to reason, plan, and act on the decisions we make is itself a [End Page 235] part of our chaotically determined neurologic system. When we are healthy, we are able to reason in our best interests and act on those reasons. This is modeled as an ability for the organism to metaphorically "move about" the map of its own possibilities, and more important, to both enter and escape certain states, known as chaotic attractors, into which it is likely to be drawn. "Where" we wind up, psychologically speaking, at any point in time is determined by our own system, and so we may say that in such a case we are autonomous and our choices are made freely. Depression, on the other hand, can be compared to a deep groove in the map, a chaotic attractor that is hard to escape, and so the system quite literally becomes "stuck in a rut." This is subjectively experienced as the tendency for thought processes and activities to fall into negative and self-defeating patterns despite the best efforts of the client to escape these habits. So long as the organism does not have a sense of being "trapped" in an attractor (whether a depressive or, for example, manic or compulsive state), then that organism may be said to be free. Medication and the therapy that accompanies it, so far as it facilitates our ability to escape deep chaotic attractors, promotes our own freedom of will. If a car cannot spin its way out of a ditch, does the tow truck hinder or promote its freedom by hauling it back onto solid pavement where it may again... (shrink)

Reductionism and complexity theory are two paradigms frequently found in language research. There exist a number of conflicts in terms of concepts and methodologies between reductionism and complexity theory, which are not conducive to creating a unified language research framework. This paper starts by discussing the adaptability of complex dynamic systems and combines cognitive processing model and artificial neural networks to construct and verify an adaptive weight model, showing that the study of reductionism is induction of high-weight elements and the (...) study of complexity theory is a discussion of system complexity from adaptability, meaning that there is a good fit between the two frameworks. The adaptive weight model is conducive to developing a unified interpretation of language research results. (shrink)

We present a new viable nonlinear chaotic paradigm. This paradigm has four nonlinear terms. The essential features of the new paradigm have been investigated. Our new system is confirmed to have chaotic behaviors by calculating its Lyapunov exponents. The relations of the system states are displayed by a suggested new signal flow graph. The proposed SFG is discussed via some graph theory tools, and some of its hidden features are calculated. In addition, the system is realized via constructing (...) its electronic circuit which helps in the real applications. Also, a robust controller for the system is designed with the aid of a genetic algorithm. (shrink)

In "Comparative Literature, Variation Theory, and a New Construction of World Literature" Wang Chao discusses Shunqing Cao's "variation theory" as a framework in the discipline of comparative literature and its applicability for a new construction of world literature. Wang argues that Goethe's concept of world literature can be expanded and developed for a new construction of the idea of world literature. Wang's principal argument is that comparative literature in today's heterogeneity and cross-cultural variabilities can be revived with the notions of (...) variation and its connecting aspect of world literature. Both variation theory and perspectives of the concept of "new world literature" are based in recent insights in comparative literature, on variations of literary exchange, on interpretation in cross-civilization literary circulation, translation, and production. Wang proposes that these views broaden and adjust the boundary of comparability, thus injecting much-needed vitality into comparative literature and world literature research. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 229-234 [Access article in PDF] Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View Gordon Globus Keywords nonlinear dynamics, modernity, postmodernity, quantum brain theory, free will, self-organization, autopoiesis, autorhoesis Although nonlinear dynamical conceptu-alizations have been applied to psychia-try for over 20 years,1 they have not had significant impact on the field. Unfortunately Heinrichs' very thoughtful contribution (...) to the discussion is unlikely to move such disinterest. Pragmatically successful paradigms in the phase of Kuhnian "normal science" are highly resistant to change. There is no crisis that besets triumphalist biological psychiatry that might lead to clinical or scientific revolution. At the same time, as I suggest at the end of this commentary, the ideas of nonlinear dynamics may not be revolutionary enough, remaining staunchly within the framework of modernity.In what follows I discuss four issues related to Heinrichs' article. First, I try to enrich his presentation of nonlinear dynamics by bringing in the role of self-organization in the evolution of nonlinear dynamical brain systems and by making the nonlinear dynamics "tunable." Second, I discuss whether Heinrichs succeeds in avoiding the dualism of the biopsychosocial model that he criticizes. Third, I look at the issue of "free will," which Heinrichs would understandably like to avoid. Finally, I mention a new form of dynamics, namely thermofield dynamics, which I think is more promising than nonlinear dynamics. Self-Organizing Self-Tuning Nonlinear Dynamical Systems In the case of psychiatry, we are not considering nonlinear dynamical systems like the weather or an ecosystem, but the brain's neural networks in terms of nonlinear dynamics with all its chaos. There is a principle of such systems of neural networks that Heinrichs does not bring out, although it is extremely important for them. These systems are self-organizing under a Hamiltonian principle of "least energy." To use Hopfield and Tank's (1986) terms, nonlinear dynamical neural networks self-organize toward attractors that minimize the "computational energy" of the system, or for Smolensky (1988), self-organize toward "harmony," or for Globus (1995, 2003), in a Heideggerian vein, self-organize to maximize "belonging-together." In this elaborated framework, rational deliberation is one constraint among many on a self-organizing nonlinear dynamical process. [End Page 229]Heinrichs brings out beautifully the nonlinear dynamical way of thinking clinically. This is not the dynamics of mechanistic psychodynamics, which features psychological forces in vectorial conflict—id versus superego and their compromises—but a flowing evolution of states in which small changes in initial state may have large effects (nonlinearity) on the state trajectory. To live a life is often to feel surprise, which nonlinear dynamics with its chaotic regimes well portrays.But there is a way that classical Freud and nonlinear dynamical neural networks do come together—in the "economics," discharges and conservations of libidinal energy, expenditures and credits in Derrida's (1978) accounting. Heinrichs does not mention this similarity. The economic principles differ between Freud's late nineteenth-century thermodynamics and Heinrichs' late twentieth-century nonlinear dynamics, it is true, but it is all economics.Freud called this economic functioning the "pleasure principle" in which "libido" seeks to discharge its instinctual energy store, reducing the level of instinctual tension. This "primary process" proceeds to an attractor by the quickest, most direct way possible, whereas the "secondary process" defers reduction in instinctual tension, subjecting the primary process to thought. Self-organizing directly to the attractor is the primary process with which the secondary process interferes, introducing deferral.The economy of nonlinear dynamics pictures a "landscape," a variegated topography with peaks and valleys. Each point on the topography represents a state. Peak points are repellors—for example, states in which the phobic object is approached—and the lowest points of the valleys are attractors—for example, obsessions and compulsions. The path of occupied states self-organizes away from repellors and toward attractors. This topography is an energy landscape. Its dynamics spontaneously tends—"self-organizes"—toward least energy/high-constraint satisfaction. Freud's pleasure principle is just the Hamiltonian least energy... (shrink)

The author proposes to add another dichotomy to the list of essential tensions proposed by Professor Duda, namely beauty and ugliness. Physicists believe that only beautiful theories describe the world correctly, and that General Relativity is one of the most beautiful physical theories. The author explains why physicists regard this theory as beautiful.

A number of authors have recently argued that the mathematical insights of "chaos theory" offer a promising formal model or significant analogy for understanding at least some historical events. We examine a representative claim of each kind regarding the application of chaos theory to problems of historical explanation. We identify two lines of argument. One we term the Causal Thesis, which states that chaos theory may be used to plausibly model, and so explain, historical events. The other (...) we term the Convergence Thesis, which holds that, once the analogy between history and chaos theory is properly appreciated, any temptation to divide history from the rest of science should be greatly lessened. We argue that the proffered analogy between chaos theory and history falls apart upon closer analysis. The promised benefits of chaos theory vis-à-vis history are either fantastic or, at best, an extremely loose heuristic which, while retaining nothing of the considerable intrinsic interest of nonlinear dynamics, easily seduces the unwary into taking at face value terms and concepts that have a specifically precise meaning only within the confines of mathematical theory. (shrink)

To describe and analyze the unstable periodic orbits of the Rucklidge system, a so-called symbolic encoding method is introduced, which has been proven to be an efficient tool to explore the topological properties concealed in these periodic orbits. In this work, the unstable periodic orbits up to a certain topological length in the Rucklidge system are systematically investigated via a proposed variational method. The dynamics in the Rucklidge system are explored by using phase portrait analysis, Lyapunov exponents, and Poincaré (...) first return maps. Symbolic encodings of the periodic orbits with two and four letters based on the trajectory topology in the phase space are implemented under two sets of parameter values. Meanwhile, the bifurcations of the periodic orbits are explored, significantly improving the understanding of the dynamics of the Rucklidge system. The multiple-letter symbolic encoding method could also be applicable to other nonlinear dynamical systems. (shrink)

Dynamical systems theory (DST) is a branch of mathematics that assesses abstract or physical systems that change over time. It has a quantitative part (mathematical equations) and a related qualitative part (plotting equations in a state space). Nonlinear dynamical systems theory applies the same tools in research involving phenomena such as chaos and hysteresis. These approaches have provided different ways of investigating and understanding cognitive systems in cognitive science and neuroscience. The ‘dynamical hypothesis’ claims that cognition is and (...) can be understood as dynamical systems. Common consequences for such an approach include rejecting understanding cognition as information processing in nature, including eschewing explanatory roles for computation or representation. Contemporary applications of DST include mouse‐tracking studies in cognitive science and nonrepresentational perspectives on motor control in neuroscience. Such work has philosophical implications concerning the boundaries of cognition, explanation, and representations. DST offers powerful methodology and theories that raise many topics of philosophical significance. (shrink)

A double delayed hybrid stochastic prey-predator bioeconomic system with Lévy jumps is established and analyzed, where commercial harvesting on prey and environmental stochasticity on population dynamics are considered. Two discrete time delays are utilized to represent the maturation delay of prey and gestation delay of predator, respectively. For a deterministic system, positivity of solutions and uniform persistence of system are discussed. Some sufficient conditions associated with double time delays are derived to discuss asymptotic stability of interior equilibrium. For a (...) stochastic system, existence and uniqueness of a global positive solution are studied. By using the invariant measure theory and singular boundary theory of diffusion process, existence of stochastic Hopf bifurcation and stochastic stability are investigated. By constructing appropriate Lyapunov functions, asymptotic dynamic behavior of the proposed hybrid stochastic system with double time delays and Lévy jumps is discussed. Numerical simulations are provided to show consistency with theoretical analysis. (shrink)

We explore success drivers of reward-based crowdfunding for poverty alleviation in China. The results from our econometric modeling using data from 4375 reward-based crowdfunding campaigns suggest that poverty alleviation campaigns, as compared to ordinary ones, benefit from higher funded amounts, larger backer numbers, and greater success rates. The results also suggest that poverty alleviation campaigns perform better when the products sold originate from poorer (as compared to wealthier) regions and when price premiums are lower (as compared to higher). We corroborate (...) important findings from the field study with an experimental study, showing that the consumer’s feeling of warm glow accounts for the positive effects of poverty alleviation campaigns (as compared to ordinary) campaigns. We expand the applications of warm-glow theory into the context of reward-based crowdfunding campaigns for poverty alleviation and offer new insights into success drivers of such campaigns. (shrink)

We designed an experiment to test the application of optimality theory (OT) in kinship terminology studies. Specifically, we examined the OT constraints within a set of behavioral data using Chinese kin terms. The results from this behavioral approach support and extend Jones' linguistic approach by identifying underlying cognitive mechanisms that can explain and predict behavioral responses in kinship identification.

Tradition wireless sensor networks transmit data by single or multiple hops. However, some sensor nodes close to a static base station forward data more frequently than others, which results in the problem of energy holes and makes networks fragile. One promising solution is to use a mobile node as a mobile sink, which is especially useful in energy-constrained networks. In these applications, the tour planning of MS is a key to guarantee the network performance. In this paper, a novel (...) strategy is proposed to reduce the latency of mobile data gathering in a WSN while the routing strategies and tour planning of MS are jointly optimized. First, the issue of network coverage is discussed before the appropriate number of clusters being calculated. A dynamic clustering scheme is then developed where a virtual cluster center is defined as the MS sojourn for data collection. Afterwards, a tour planning of MS based on prediction is proposed subject to minimizing the traveling distance to collect data. The proposed method is simulated in a MATLAB platform to show the overall performance of the developed system. Furthermore, the physical tests on a test rig are also carried out where a small WSN based on an unmanned aerial vehicle is developed in our laboratory. The test results validate the feasibility and effectiveness of the method proposed. (shrink)

I take the phrase ''the theory of nonlinear oscillations'' to identify a historical phenomenon. Under this heading a powerful school in Soviet science, L. I. Mandelstam's school, developed its version of what was later called ''nonlinear dynamics''. The theory of nonlinear oscillations was formed around the concept of self-oscillations, which was elaborated by Mandelstam's graduate student A. A. Andronov. This concept determined the paradigm of the theory of nonlinear oscillations as well as its ideology, that (...) is, a set of characteristic ideas which, together with the corresponding examples and analogues, allowed the expansion of the theory into associated areas where it indicated new interesting phenomena and posed new problems. It was the ideology that made possible the broader application of the theory of nonlinear oscillations, whose domain was originally lumped systems, to continuous media and its subsequent progress toward synergetics. In the course of its ideological application, the concept of self-oscillations was greatly extended, became vague and diffuse, and related concepts such as self-waves and self-structures appeared. (shrink)

In this paper, we propose a nonlinear coupled model to study the two interacting processes of awareness diffusion and epidemic spreading on the same individual who is affected by different neighbor behavior status on multiplex networks. We achieve this topology scenario by two kinds of factors, one is the perception factor that can change interplay between different layers of networks and the other is the neighbors’ behavior status that can change the infection rate in each layer. According to the (...) microscopic Markov chain approach, we analyze the dynamical evolution of the system and derive the theoretical epidemic threshold on uncorrelated heterogeneous networks, and then, we validate the analysis by numerical simulation and discuss the final size of awareness diffusion and epidemic spreading on a scale-free network. With the outbreak of COVID-19, the spread of epidemic in China prompted drastic measures for transmission containment. We examine the effects of these interventions based on modeling of the awareness-epidemic and the COVID-19 epidemic case. The results further demonstrate that the epidemic spreading can be affected by the effective transmission rate of the awareness and neighbors’ behavior status. (shrink)

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject (...) from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selected book exercises. See www.cambridge.org/economics/resources. (shrink)

The unified theory of dose and effect, as indicated by the median-effect equation for single and multiple entities and for the first and higher order kinetic/dynamic, has been established by T.C. Chou and it is based on the physical/chemical principle of the massaction law (J. Theor. Biol. 59: 253-276, 1976 (質量作用中效定理) and Pharmacological Rev. 58: 621-681, 2006) (普世中效指數定理). The theory was developed by the principle of mathematical induction and deduction (數學演繹歸納法). Rearrangements of the median-effect equation lead to Michaelis-Menten, Hill, Scatchard, (...) and Henderson-Hasselbalch equations. The “median” serves as the universal reference point and the “common link” for the relationship of all entities and is also the “harmonic mean” of kinetic dissociation constants. Over 300 mechanism-specific equations have been derived and published using the mathematical induction-deduction process. These equations can be deduced into several general equations, including the median-mediated whole/part equation, combination index theorem, isobologram equation, and polygonogram. It is proven that “dose” and “effect” are interchangeable, thus, “substance” and “function” are interchangeable, which leads to “the unity theory” (劑效、心物、知行一元論) in quantitative mathematical philosophy (數學的定量哲學) in functional context. Therefore, a general theory centered on the “median” and based on equilibrium dynamics has evolved. In other words: [「中」的宇宙觀： 以「中」爲基凖的動力學生態平衡]. Based on the median-effect equation of the mass-action law, the fundamental claim is that we can draw “a specific cure” for only two data points, if they are determined accurately. This claim has far reaching consequences since it defies the general held belief that two points can dray only a straight line. Remarkably, the unity theory (一元論) providesscientific/mathematical interpretation in equations and in graphics of Chinese ancient philosophy, including Fu-Si Ba Gua (伏羲八卦), Dao’s Harmony (和諧), the Confucian doctrine of the mean (儒家中庸之道), Chou Dun-Yi’s (周敦頤, 1017-1073) From Wu-ji to Tai-ji and Taiji Tu Sho (無極而太極及太極圖說). The moderntopological analysis for trinity yields an exact correspondence to the Ba-Gua, which was introduced over 4,000 years ago. Furthermore, the median-centered algorithm, promotes modern ecological content (生態學) in the equilibral dynamic state of harmony. It is concluded that Western science and Eastern philosophy are directly linked and complementary to each other. Since the truth in mathematical quantitative philosophy (數學的定量哲學) has no boundaries, East and West philosophies can flourish together for the common goal and ideal in science and in humanity (世界大同). (shrink)

v. 1. Theory of continuous Fokker-Planck systems -- v. 2. Theory of noise induced processes in special applications -- v. 3. Experiments and simulations.

This article argues that the process of development as such explains a great deal of the forms and properties of individual developmental trajectories, without the necessity of having to rely on either external or internal factors or causes. Both the problem of developmental change and invariance can be explained by employing a dynamic systems conceptualization of development. It is shown that dynamic systems models on the one hand and those of the genuine developmental models in psychology on the other, share (...) a set of important general properties that are able to explain both the universal and the idiosyncratic aspects of developmental processes. The concept of mental and behavioral ecology, which may serve as a starting point for specific theories of development of cognition, social behavior, personality and so forth, is discussed. It is concluded that both long-term and short-term developmental patterns will be shown to follow similar abstract dynamical principles. (shrink)

In the context of coronavirus pandemic, the face-recognition-based access control system has been intensively adopted to protect students’ and teachers’ health and safety in school. However, the impact of FACS, as a new technology, on students’ attitude toward accepting FACS has remained unknown from the psychological halo effect. Drawn on “halo effect” theory where psychological effects affect the sense of social identity and belonging, the present study explored college students’ sense of school identity and belonging in using FACS during COVID-19 (...) based on the technology acceptance model. Data collected from 391 college students was analyzed using SEM to verify the relationship among perceived usefulness, perceived ease of use, intention to use, school identity, and school belonging. The results show that PU and PEU can positively predict IU, and consequentially can positively predict school identity and school belonging. Our study expands the application of halo effect theory to study FACS acceptance based on TAM, and provides strong evidence to support the effect of school FACS during the pandemic. The findings of this study also suggest that FACS acceptance can enhance students’ sense of school identity and belonging. (shrink)

BackgroundDrawing from Erikson’s theory, Domino and Affonso constructed the Inventory of Psychosocial Balance, a scale with satisfactory reliability and validity. However, the lack of a credible Chinese version of the scale may hinder research on ego development in Taiwan. The aim of the present study was to construct a short form Chinese IPB. In addition, factor analysis was employed to shorten the original 120-item scale to make it suitable for application in the older adults in the future.MethodsThe study involved three (...) steps: The first step was to establish the 120-items of the Chinese Inventory of Psychosocial Balance, and we conducted translation, back-translation, expert validity, and reliability of pilot study for this step. Following the first step was to construct the short-form C-IPB in the second step, and the CIPB-SF was developed via item analysis and factor analysis. Finally, we assessed the reliability and validity of the CIPB-SF via structural equation model in the third step.ResultsThree hundred eight older adults without cognitive disorder completed the IPB. The 40-item CIPB-SF was completed through item analysis and factor analysis. The internal consistency test of CIPB-SF and the eight stages were good. The CIPB-SF had acceptable validity, except in the intimacy and identity stages, in which validity was only fair. Compared with the IPB, the CIPB-SF had good reliability and acceptable validity. However, because of its conciseness, the 40-item CIPB-SF was more suited for application among the Chinese elderly population because its application avoids physical overload.ConclusionThe CIPB-SF served as a concise scale for assessing ego development in our study. This scale can also serve as a useful tool for convenient screening in the future. (shrink)

The scientific study of chaotic dynamics, popularly known as chaos theory, has been described by several writers as a revolution in the sense of Kuhn. I provide a definition of chaos theory and offer a brief description of this field of research. I then take up the question of whether or not chaos theory should be described as "revolutionary," in light of the fact that no well-developed science of nonlinear dynamics preceded it. In some (...) respects, chaos theory may be fruitfully described as an "immature science," and the semantic view of theories helps to bring out some of its important features. Many aspects of this emerging field make it most appropriate to consider it a new style of scientific reasoning, analogous to statistical thinking as interpreted by Ian Hacking. (shrink)

The analysis of physical and biological systems through models and mathematics of chaotic behavior and nonlinear dynamics rose to prominence in the 1980s. Many authors, most notably Ilya Prigogine and Isabelle Stengers, made glancing references to applications of this new paradigm to the social and historical sciences, but little fruit was harvested until this decade. Physiologists studying irregular heart rhythms, psychologists examining brain activity, biologists graphing population trends, economists tracking stock price movements, military strategists assessing the outbreak (...) of wars, and sociologists modeling the rise of cities, found nonlinear dynamics refreshingly stimulating in reevaluating old theories and creating new ones. Modeling the past was an inevitable extension of this trend, and theorizing on the new historiography soon followed, with the terms of the debate outlined from 1990 to 1993 by Alan Beyerchen, Katherine Hayles, Stephen Kellert, Charles Dyke, myself, and, in the pages of History and Theory, by George Reisch and Donald McCloskey. The subject of "the chaos of history" is now enjoying a healthy exchange of ideas from all sides. This essay: reviews the precedence for integrating chaos and history; gives a brief history of this integration including an evaluation of a critique of Reisch and McCloskey by Roth and Ryckman, and presents a metahistory of how chaos theory explains its own development; defends a chaotic model of historical sequences; gives a specific historical example of nonlinear history; explores the latest trends in the field of self-organization, antichaos, simplexity, and feedback mechanisms, providing data to show that modern and historical social movements change in a parallel fashion; and exorcises Laplace's demon by showing it was always a chimera. (shrink)

The analysis of physical and biological systems through models and mathematics of chaotic behavior and nonlinear dynamics rose to prominence in the 1980s. Many authors, most notably Ilya Prigogine and Isabelle Stengers, made glancing references to applications of this new paradigm to the social and historical sciences, but little fruit was harvested until this decade. Physiologists studying irregular heart rhythms, psychologists examining brain activity, biologists graphing population trends, economists tracking stock price movements, military strategists assessing the outbreak (...) of wars, and sociologists modeling the rise of cities, found nonlinear dynamics refreshingly stimulating in reevaluating old theories and creating new ones. Modeling the past was an inevitable extension of this trend, and theorizing on the new historiography soon followed, with the terms of the debate outlined from 1990 to 1993 by Alan Beyerchen, Katherine Hayles, Stephen Kellert, Charles Dyke, myself, and, in the pages of History and Theory, by George Reisch and Donald McCloskey. The subject of "the chaos of history" is now enjoying a healthy exchange of ideas from all sides. This essay: reviews the precedence for integrating chaos and history; gives a brief history of this integration including an evaluation of a critique of Reisch and McCloskey by Roth and Ryckman, and presents a metahistory of how chaos theory explains its own development; defends a chaotic model of historical sequences; gives a specific historical example of nonlinear history; explores the latest trends in the field of self-organization, antichaos, simplexity, and feedback mechanisms, providing data to show that modern and historical social movements change in a parallel fashion; and exorcises Laplace's demon by showing it was always a chimera. (shrink)

The theory of nonlinear complex systems has become a successful and widely used problem-solving approach in the natural sciences - from laser physics, quantum chaos and meteorology to molecular modeling in chemistry and computer simulations of cell growth in biology. In recent times it has been recognized that many of the social, ecological and political problems of mankind are also of a global, complex and nonlinear nature. And one of the most exciting topics of present scientific and (...) public interest is the idea that even the human mind is governed largely by the nonlinear dynamics of complex systems. In this wide-ranging but concise treatment Prof. Mainzer discusses, in nontechnical language, the common framework behind these endeavours. Special emphasis is given to the evolution of new structures in natural and cultural systems and it is seen clearly how the new integrative approach of complexity theory can give new insights that were not available using traditional reductionistic methods. (shrink)

Due to the individual differences controlling brain-computer interfaces, the applicability and accuracy of BCIs based on motor imagery are limited. To improve the performance of BCIs, this article examined the effect of transcranial electrical stimulation on brain activity during MI. This article designed an experimental paradigm that combines tES and MI and examined the effects of tES based on the measurements of electroencephalogram features in MI processing, including the power spectral density and dynamic event-related desynchronization. Finally, we investigated the effect (...) of tES on the accuracy of MI classification using linear discriminant analysis. The results showed that the ERD of the μ and β rhythms in the left-hand MI task was enhanced after electrical stimulation with a significant effect in the tDCS group. The average classification accuracy of the transcranial alternating current stimulation group and transcranial direct current stimulation group were improved significantly compared to the pre-and pseudo stimulation groups. These findings indicated that tES can improve the performance and applicability of BCI and that tDCS was a potential approach in regulating brain activity and enhancing valid features during noninvasive MI-BCI processing. (shrink)

In speaker recognition systems, feature extraction is a challenging task under environment noise conditions. To improve the robustness of the feature, we proposed a multiscale chaotic feature for speaker recognition. We use a multiresolution analysis technique to capture more finer information on different speakers in the frequency domain. Then, we extracted the speech chaotic characteristics based on the nonlinear dynamic model, which helps to improve the discrimination of features. Finally, we use a GMM-UBM model to develop a speaker recognition (...) system. Our experimental results verified its good performance. Under clean speech and noise speech conditions, the ERR value of our method is reduced by 13.94% and 26.5% compared with the state-of-the-art method, respectively. (shrink)

Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory (...) treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. (shrink)

Based on the existing financial system risk models, a set of time-lag financial system risk models is established considering the influence brought by time-lag factors on the financial risk system, and the dynamical behavior of this system is analyzed by using chaos theory. Through Matlab simulation, the bifurcation diagram and phase diagram of time-lag risk intensity and control intensity are plotted. The analysis shows that this kind of time-lag financial system risk model has complex dynamic behavior, different motion states (...) will appear when different parameter values are selected, and the time-lag risk intensity parameter also has a very strong influence on the system motion. To ensure the operation of the financial system in a stable state, measures with certain delay effects must be taken to control the risk and to choose the appropriate time-lag control intensity, and too much or too little time-lag control intensity is not conducive to the benign operation of the system. (shrink)

The probability ranking conclusion is an extension of the absolute form evaluation conclusion. Firstly, the random simulation evaluation model is introduced; then, the general idea of converting the traditional evaluation method to the random simulation evaluation model is analyzed; on this basis, based on the rule of “further ensuring the stability of the ranking chain on the basis of increasing the possibility of the ranking chain,” two methods of solving the probability ranking conclusion are given. Based on the rule of (...) “further guaranteeing the stability of the ranking chain on the basis of improving the likelihood of the ranking chain,” two methods are given to solve the likelihood conclusion. This paper argues that this absolute form of conclusion hinders the approximation of the theory to the essence of the actual problem and is an important reason for the problem of “non-consistency of multi-evaluation conclusions.” To address this problem, a stochastic simulation-based comprehensive evaluation solution algorithm based on the idea of “Monte Carlo simulation” is proposed, and the corresponding ranking method is investigated, which is characterized by generating evaluation conclusions with probability information, and thus has more advantages than the absolute conclusion form in terms of problem interpretability. The method is characterized by the generation of evaluation conclusions with probabilistic information and thus has more advantages than the absolute conclusion form in terms of problem interpretation. Because of the independence of the stochastic simulation solution method, it is applied to the “bottom-up” evaluation model as an example, and a novel autonomous evaluation method is constructed. Finally, the application of the stochastic simulation evaluation model is illustrated by an example and compared with the absolute form evaluation. The evaluation model is an extension of the traditional evaluation model, which can further broaden the practical application of comprehensive evaluation theory. (shrink)

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least (...) time, the principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

The unreduced solution to the arbitrary interaction problem, absent in the standard theory framework, reveals many equally real and mutually incompatible system configurations, or "realizations". This is the essence of universal dynamic undecidability, or multivaluedness, and the ensuing causal randomness (unpredictability), non-computability, irreversible time flow (evolution, emergence), and dynamic complexity of every real system, object, or process. This creative undecidability of real-world dynamics provides causal explanations for "quantum mysteries", relativity postulates, cosmological problems, and the huge efficiency of high-complexity phenomena, (...) such as life, intelligence, and consciousness, giving rise to extended applications, far beyond the critical limits of usual science paradigm. (shrink)