On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of (...) Shannon's communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)

This article deals with the control of chaos on the convective motion in a ferrofluid filled in a rotating porous medium and under the helical force effect. We performed a truncated expansion of Galerkin and found the Lorenz-type model which described the system. The dynamical system is characterized using appropriate and subsequent criteria. We noticed that the system presents regular and chaotic behaviors according to the parameters at present. A considerable reduction of the chaotic domain is noticed with (...) the increase of the intensity of the helical force and of the Darcy number, thus making it possible to delay the heat transfer in the system. The increase in the viscosity ratio and the Taylor number widen the chaotic domain leading to an acceleration of the heat transfer in the system. (shrink)

In this research work, we formulate the phenomena of the financial system in the fractional framework to describe the complex nature of finance. The basic definitions and ideas of the Caputo-Fabrizio fractional operator are listed. We introduce a novel numerical technique for the dynamical behaviour of our fractional model. The oscillatory and chaotic behaviour of the model is studied with the variation of various input parameters on the model. We have shown that there exists strong oscillatory and chaotic (...) behaviour in the system; moreover, we highlighted the impact of fractional-order parameter on the model. The conditions for the local complex behaviour of the system are analyzed with the impact of certain parameters on the macroeconomic. Our findings suggest that the values of initial conditions, fractional order, and input parameters can lessen the chaos of the proposed financial system. (shrink)

Chaos theory is a rapidly growing field. As a technical term, chaos refers to deterministic but unpredictable processes being sensitively dependent upon initial conditions. Neurobiological models and experimental results are very complicated and some research groups have tried to pursue the neuronal chaos. Babloyantz's group has studied the fractal dimension (d) of electroencephalograms (EEG) in various physiological and pathological states. From deep sleep (d=4) to full awakening (d>8), a hierarchy of strange attractors paralles the hierarchy of states of consciousness. In (...) epilepsy (petit mal), despite the turbulent aspect of a seizure, the attractor dimension was near to 2. In Creutzfeld-Jacob disease, the regular EEG activity corresponded to an attractor dimension less than the one measured in deep sleep. Is it healthy to be chaotic? An active desynchronisation could be favourable to a physiological system. Rapp's group reported variations of fractal dimension according to particular tasks. During a mental arithmetic task, this dimension increased. In another task, a P300 fractal index decreased when a target was identified. It is clear that the EEG is not representing noise. Its underlying dynamics depends on only a few degrees of freedom despite yet it is difficult to compute accurately the relevant parameters.What is the cognitive role of such a chaotic dynamics? Freeman has studied the olfactory bulb in rabbits and rats for 15 years. Multi-electrode recordings of a few mm2 showed a chaotic hierarchy from deep anaesthesia to alert state. When an animal identified a previously learned odour, the fractal dimension of the dynamics dropped off (near limit cycles). The chaotic activity corresponding to an alert-and-waiting state seems to be a field of all possibilities and a focused activity corresponds to a reduction of the attractor in state space. For a couple of years, Freeman has developed a model of the olfactory bulb-cortex system. The behaviour of the simple model without learning was quite similar to the real behaviour and a model with learning is developed. (shrink)

In this paper, we investigate the ultimate bound set and positively invariant set of a 3D Lorenz-like chaotic system, which is different from the well-known Lorenz system, Rössler system, Chen system, Lü system, and even Lorenz system family. Furthermore, we investigate the global exponential attractive set of this system via the Lyapunov function method. The rate of the trajectories going from the exterior of the globally exponential attractive set to the interior of the globally exponential attractive set is also (...) obtained for all the positive parameters values a,b,c. The innovation of this paper is that our approach to construct the ultimate bounded and globally exponential attractivity sets assumes that the corresponding sets depend on some artificial parameters ; that is, for the fixed parameters of the system, we have a series of sets depending on λ and m. The results contain the known result as a special case for the fixed λ and m. The efficiency of the scheme is shown numerically. The theoretical results may find wide applications in chaos control and chaos synchronization. (shrink)

This is the first work to apply complex systems science to the psychological interplay of order and chaos. The author draws on thought from a wide range of disciplines-both conventional and unorthodox-to address such questions as the nature of consciousness, the relation between mind and reality, and the justification of belief systems. The material should provoke thought among systems scientists, theoretical psychologists, artificial intelligence researchers, and philosophers.

New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the (...) Perron–Frobenius operator, is derived. It leads to a simple interpretation in terms of classical resonances. The theory is applied to zeros of the Riemann zeta function. A striking correspondence between the associated classical dynamical zeta functions and the Riemann zeta itself is found. This induces a resurgence phenomenon where the lowest Riemann zeros appear replicated an infinite number of times as resonances and sub-resonances in the spacing autocovariances. The theoretical results are confirmed by existing “data.” The present work further extends the already well known semiclassical interpretation of properties of Riemann zeros. (shrink)

Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamical systems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among “exotic” attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda (...) and Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given. Key Words: Cantor coding; chaotic itinerancy; dynamic aspects of the brain; dynamic associative memory; episodic memory; high-dimensional dynamical systems; SCND attractors. (shrink)

This paper is expected to introduce a novel memductor-based chaotic system. The local dynamical entities, such as the basic dynamical behavior, the divergence, the stability of equilibrium set, and the Lyapunov exponent, are all investigated analytically and numerically to reveal the dynamic characteristics of the new memductor-based chaotic system as the system parameters and the initial state of memristor change. Subsequently, an active control method is derived to study the synchronous stability of the novel memductor-based chaotic (...) system through making the synchronization error system asymptotically stable at the origin. Further to these, a memductor-based chaotic circuit is designed, realized, and applied to construct a new memductor-based secure communication circuit by employing the basic electronic components and memristor. Furthermore, the design principle of the memductor-based chaotic circuit is thoroughly analyzed and the concept of “the memductor-based chaotic circuit defect quantification index” is proposed for the first time to verify whether the chaotic output is consistent with the mathematical model. A good qualitative agreement is shown between the simulations and the experimental validation results. (shrink)

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

This text explores how we understand living and other complex systems. The conventional basis of understanding rests on abstract general theories, but this book proposes conceptual continuity as a new means of comparing systems of divergent complexity and resolving problems in complex systems.

We demonstrate by use of a simple one-dimensional model of a square barrier imbedded in an infinite potential well that decoherence is enhanced by chaotic-like behavior. We, moreover, show that the transition h→0 is singular. Finally it is argued that the time scale on which decoherence occurs depends, on the degree of complexity of the underlying quantum mechanical system, i.e., more complex systems decohere relatively faster than less complex ones.

In a previous essay I argued that quantum chaos cannot be exhibited in models of quantum systems within von Neumann's mathematical framework for quantum mechanics, and that it can be exhibited in models within Dirac's formal framework. In this essay, the negative thesis concerning von Neumann's framework is elaborated further by extending it to the case of Hamiltonian operators having a continuous spectrum. The positive thesis concerning Dirac's formal framework is also elaborated further by constructing a chaotic model (...) of an open quantum system in which an entropy measure is shown to approach its maximum value as time goes to infinity. Having such an entropy measure is a characteristic that is closely connected to chaotic behavior in phase space models of classical systems. (shrink)

This text addresses the problems of complex systems in understanding natural phenomena and the behaviour of systems related to human activity, from a science and humanities perspective. It discusses molecular behaviour and structures, and offers examples of ecological and environmental modelling.

This book explores the theories of chaos and complexity as applied to a variety of disciplines including political science, organizational and management science, economics, and education.

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various (...) class='Hi'>chaotic and periodic behaviors, are analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied. (shrink)

Introduction to complexity and complex systems -- Introduction to large linear systems -- Introduction to biochemical oscillators and nonlinear biochemical systems -- Modularity, redundancy, degeneracy, pleiotropy and robustness in complex biological systems -- The evolution of biological complexity; invertebrate immune systems -- Irreducible and specified complexity in living systems -- The complex adaptive and innate human immune systems -- Complexity in quasispecies : microRNAs -- Introduction to complexity in economic systems -- Complexity (...) in quasispecies : micrornas -- Dealing with complexity. (shrink)

Ritualized behavior, intuitively recognizable by its stereotypy, rigidity, repetition, and apparent lack of rational motivation, is found in a variety of life conditions, customs, and everyday practices: in cultural rituals, whether religious or non-religious; in many children's complicated routines; in the pathology of obsessive-compulsive disorders (OCD); in normal adults around certain stages of the life-cycle, birthing in particular. Combining evidence from evolutionary anthropology, neuropsychology and neuroimaging, we propose an explanation of ritualized behavior in terms of an evolved Precaution (...) System geared to the detection of and reaction to inferred threats to fitness. This system, distinct from fear-systems geared to respond to manifest danger, includes a repertoire of clues for potential danger as well as a repertoire of species-typical precautions. In OCD pathology, this system does not supply a negative feedback to the appraisal of potential threats, resulting in doubts about the proper performance of precautions, and repetition of action. Also, anxiety levels focus the attention on low-level gestural units of behavior rather than on the goal-related higher-level units normally used in parsing the action-flow. Normally automatized actions are submitted to cognitive control. This “swamps” working memory, an effect of which is a temporary relief from intrusions but also their long-term strengthening. Normal activation of this Precaution System explains intrusions and ritual behaviors in normal adults. Gradual calibration of the system occurs through childhood rituals. Cultural mimicry of this system's normal input makes cultural rituals attention-grabbing and compelling. A number of empirical predictions follow from this synthetic model. (Published Online February 8 2007) Key Words: childhood ritual; compulsion; event boundaries; evolutionary psychology; obsessive-compulsive disorder; ritual; thought intrusion. (shrink)

This article reports the findings of a survey examining whether gender differences influence the degree to which individuals recognize unethical conduct in the use and development of information technology. The results show that, on the average, there is a significant gender gap in the recognition of unethical behavior in information systems. Although, women are better able to recognize unethical actions described in information systems scenarios than men, the existence of statistically significant differences varies depending upon the nature (...) of the ethical dilemma. The findings of this study provide both managers and researchers valuable understanding regarding the differences (and similarities) in the reactions of individuals of both genders to unethical situations in information systems. (shrink)

Past research has focused on individual culpability with the assumption that individuals will further their own self interest over that of the organization, given an appropriate opportunity. In contrast, this research shifts the focus from individual motivation to the influence of the formal and informal control systems of organizations on ethical behaviours. An open-ended interview approach was used to collect data. It was found that pressures within the informal system were the dominant influence in the resolution of ethical issues. (...) The dominance of the informal system, however, varies according to the economic position of the organization. (shrink)

Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, (...) the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated. (shrink)

This important study makes a convincing case for its thesis that the dramatic form of Shakespeare's plays corresponds to that of a natural system evolving to a more complex state while undergoing symmetry breaking. Drawing upon such key concepts of chaos theory as "global agency and self-similarity," the book constructs a methodology which illuminates many problematic aspects of agency in the selected comedies, tragedies, and histories it examines. Each of these genres is shown to reflect the paradoxical dynamics of a (...) chaotic system. This fresh -systems perspective- offers a serious challenge to the structuralist assumptions underlying many current literary approaches.". (shrink)

Qualitative Complexity offers a critique of the humanist paradigm in contemporary social theory. Drawing from sources in sociology, philosophy, complexity theory, 'fuzzy logic', systems theory, cognitive science and evolutionary biology, the authors present a new series of interdisciplinary perspectives on the sociology of complex, self-organizing structures.

t. 1. Le chaos, le temps, le principe anthropique -- t. 2. Les interprétations de la physique quantique -- t. 3. Complexité, vie, conscience.

We consider the significance of high-dimensional transitory dynamics in the brain and mind. In particular, we highlight the roles of high-dimensional chaotic dynamical systems as an “adequate language” (Gelfand 1989), which should possess both explanatory and predictive power of description. We discuss the methods of description of dynamic behavior of the brain. These methods have been adopted to capture the averaged or deterministic complexity, and further to allow for discussion of a new approach to capture the complexity (...) of the deviation from such an averaged complexity and also the complexity of interactive modes. We also give arguments in defense of our models for dynamic memory with chaotic itinerancy and Cantor coding. In addition, we discuss the reality that a model of the brain and mind should reflect. (shrink)

Experimental evidence and mathematical/computational models show that in many cases chaotic, nonregular oscillations are adequate to describe the dynamical behaviour of neural systems. Further work is needed to understand the meaning of this dynamical regime for modelling information processing in the brain.

The Medication Event Monitoring System (MEMS) is a relatively new device designed to overcome some of the disadvantages of traditional adherence-measuring techniques. MEMS has also been found useful in tracking adherence behaviour without the need to visit patients frequently. In this study each patient was given a pre-filled, labelled MEMS bottle and cap. Patients were monitored for 24 weeks. For patients specifically studied, there were periods when drug levels may have been low and some exhibited erratic medication-taking behaviour. It is (...) concluded that MEMS can measure adherence behaviour objectively, and so might be used to improve prescribing decisions, identify drug wastage and improve carer support. Further research is needed before the routine use of electronic medication monitoring can be recommended. (shrink)

E-Learning has proliferated throughout the education sector in recent years. Unfortunately, an unintended and undesirable aspect of e-Learning is centered on unethical behavior exhibited by students engaged in technology-facilitated cheating. Interestingly, cheating in e-Learning systems occurs in the social context of the class. Using results from a qualitative field study, the authors investigate the socio-technical dimensions of ethical decision-making in e-Learning systems focusing on individual and situational factors. They developed propositions and provide an in-depth discussion of identified (...) factors. Their findings provide the basis for researchers to develop testable propositions for further empirical investigations and provide insight for educators dealing with the unique challenges of the socio-technical dimensions of ethical behavior in e-Learning systems. (shrink)

In dieser Arbeit werden Ansätze aus der Hirnforschung, der Künstliche-Intelligenz-Forschung und der Chaostheorie sowie der Psychologie und der Physik kritisch hinsichtlich ihrer Aussagekraft zu bewussten mentalen Phänomenen diskutiert. Zentrale Fragestellungen richten sich dabei auf die Phänomene der Qualia und der Privatheit, das Bindungsproblem, die psycho-physische Stetigkeit und die multiple Realisierung. Während die Diskussion von Hirnforschung und Künstliche-Intelligenz-Forschung sowie Psychologie und Physik vorwiegend vor dem Hintergrund bestehender Modelle geführt wird, wird außerdem der Versuch unternommen, einen neuen Verständnisansatz auf der Grundlage chaostheoretischer (...) Begriffe zu formulieren. (shrink)

I discuss recent work in ergodic theory and statistical mechanics, regarding the compatibility and origin of random and chaotic behavior in deterministic dynamical systems. A detailed critique of some quite radical proposals of the Prigogine school is given. I argue that their conclusion regarding the conceptual bankruptcy of the classical conceptions of an exact microstate and unique phase space trajectory is not completely justified. The analogy they want to draw with quantum mechanics is not sufficiently close to (...) support their most radical conclusion. (shrink)

Open peer commentary on the article “Homeostats for the 21st Century? Simulating Ashby Simulating the Brain” by Stefano Franchi. Upshot: The target article has addressed core concepts of Ashby’s generalized homeostasis thesis as well as its relevance to building complex artificial systems. In this commentary, I discuss Ashby-inspired approaches to designing for ultrastable behaviour in robots and the extent to which complex adaptive behaviour can be underdetermined by heteronomous constraints.

In this ground-breaking work, Allan Combs presents a wide-ranging survey of the nature and origins of consciousness research, viewing consciousness as a dynamic and self-organizing process with evolutionary potential. Combs reviews the work of evolutionary theorists such as Pierre Teilhard de Chardin, Ken Wilber, Jean Gebser, and Sri Aurobindo. What emerges is a fascinating study of consciousness that discloses itself as a rich and ongoing act of self-creation, poised at the edge of chaos between past and future.

Introduction:Can nature be controlled?. Autonomous nature -- Greco-Roman concepts of nature -- Christianity and nature -- Nature personified : Renaissance ideas of nature -- Controlling nature. Vexing nature : Francis Bacon and the origins of experimentation -- Natural law : Spinoza on natura naturans and natura naturata -- Laws of nature :Lleibniz and Newton -- Epilogue : rambunctious nature in the twenty-first century.

This paper establishes a model on the upstream and downstream relationship among private enterprises, provincial and local officials, and the central government in the real estate market using the population ecology theory of mutual relations among individual species from the perspective of business ecosystem. A dynamic model is introduced and the complex dynamical behaviors of such a predator-prey model are investigated by means of numerical simulation. The local stability conditions and complex dynamics are investigated, and the existence of chaos is (...) discussed in the sense of Marotto theorem; bifurcation diagrams, Lyapunov exponents, sensitivity analysis for initial values, and time history figure of the system are mapped out and discussed. This shows that there are two routes to complicated dynamics, one of which is the cascade of flip bifurcations resulting in periodic cycles, and the other one is Neimark-Sacker bifurcation which produces attractive invariant closed curves. We arrive at conclusions that the phenomenon of chaos is harmful to private enterprises, and unstable behavior is often unfavorable. Thus, linear feedback control is applied to drive the model to a stable state when the system exhibits chaotic behaviors, achieving the goal of eliminating the negative effects to a large extent. (shrink)

In this paper, a two-level green supply chain composed of a manufacturer and a retailer is taken as the background. Considering the consumer’s double consumption preference and the manufacturer’s green product R&D investment, a differential game model of the green supply chain under the government cost subsidy strategy is constructed. Firstly, the equilibrium points of the system are solved and their stability is discussed and analyzed. Secondly, the dynamic evolution process of Nash equilibrium under the parameters of green degree, green (...) preference coefficient, retail channel preference coefficient, coefficient of the sensitivity of price, and adjustment speed are described by numerical simulation. The results show that the two ways of a system entering chaos are Flip bifurcation and N-S bifurcation, respectively, by 2D bifurcation graph, and it is also verified in 1D bifurcation diagram. When the bifurcation parameters are small, the system maintains Nash equilibrium stability. If the green degree of products is increased, the green preference coefficient will also increase; on the contrary, the retail preference coefficient will decrease. Research and development cost subsidy policy can effectively improve the green degree of products and increase the sales volume of products, so as to improve the profit of supply chain members. (shrink)

What exactly is complexity science? Two's company, three is complexity ; Disorder rules, OK? ; Chaos and all that jazz ; Mob mentality ; Getting connected -- What can complexity science do for me? Forecasting financial markets ; Tackling traffic networks and climbing the corporate ladder ; Looking for Mr./Mrs. Right ; Coping with conflict : next-generation wars and global terrorism -- Catching a cold, avoiding super-flu and curing cancer ; The mother of all complexities : our nanoscale quantum world (...) ; To infinity and beyond. (shrink)

From the Parade Child to the King of Chaos depicts the pedagogical life history of an extraordinary teacher educator and internationally renowned curriculum scholar, William E. Doll, Jr. It explores how his life experiences have contributed to the formation and transformation of a celebrated teacher educator. From the child who spontaneously led a parade to the king of chaos who embraces complexity in education, complicated tales of Doll’s journey through his childhood, youth, and decades of teaching in schools and in (...) teacher education are situated in the historical, intellectual, and cultural context of American education. Seven themes are interwoven in Doll’s life, thought, and teaching: pedagogy of play, pedagogy of perturbation, pedagogy of presence, pedagogy of patterns, pedagogy of passion, pedagogy of peace, and pedagogy of participation. Based upon rich data collected over six years, this book demonstrates methodological creativity in integrating multiple sources and lenses. Profoundly moving, humorous, and inspirational, it is a much-needed text for undergraduate and graduate courses in teacher education, curriculum studies, theory and practice of teaching and learning, life history studies, chaos and complexity theory, and postmodernism. (shrink)