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)

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)

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)

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.

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)

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)

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 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.

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 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)

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)

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.

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)

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)

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.

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)

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.

In this book, after discussing the fundamental problems of current science and other philosophic concepts, beginning with controversies between Heraclitus and Parmenides, Ilya Prigogine launches into a message of great hope: the future has not been determined. Contrary to globalisation and the apparent contemporary mass culture society, individual behaviour is beginning to increasingly become the key factor which governs the evolution of both the world and society as a whole. It is a message that challenges existing widespread views, implicitly or (...) explicitly, through mass communication, moreover the importance of the individual's actions implies a reflection of each person on the responsibilities that each one assumes when taking or acting upon a decision. This responsibility is associated with the freedom of thought as well as a critical analysis of fashions, customs, preconceived ideas, and ideologies, externally imposed: exactly contrary to the ideas of those who wish us to be "perfect consumers" in a world dominated only by monetary wealth. Challenging this drive towards the elimination of freedom of though in the individual is now imperative if we are to save man and his planet from catastrophe which seems to be ever imminent and (unfortunately) irreversible. This last book of Ilya Prigogine provides a small, disputable, but nonetheless valuable contribution towards that end. (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)

En ce XXe siècle, où la physique s'est identifiée à la science révolutionnaire par excellence, l'œuvre passionnée d'Ilya Prigogine constitue une singulière anomalie. Anormale parce qu'elle prend le parti du monde des phénomènes physiques contre le pouvoir de la théorie, jugé abusif ; mais anormale aussi par sa longue obstination à une époque où la rapidité fait foi. Le combat avait commencé au début des années soixante, sur un mode mineur : Prigogine demandait à ses collègues de reconnaître qu' " (...) il y a certainement une signification physique profonde dans l'équation de Boltzman ". Thèse apparemment bien légitime : l'équation de Boltzmann permet de décrire avec succès le comportement de non-équilibre des gaz dilués. Mais thèse iconoclaste : car, depuis que la croissance de l'entropie a été renvoyée aux seules probabilités, le comportement de non-équilibre n'est plus sensé autoriser la moindre " signification profonde ". Raconter l'histoire de ce combat, comme le fait Isabelle Stengers dans ce livre, revient à interroger les lois fondamentales sous l'angle du lien entre théorie, valeur et obligation. En effet, sans ce lien, ni la position de Prigogine ni celle des physiciens contre qui il va chercher des arguments toujours plus puissants ne sont intelligibles. L'auteur montre que ce lien permet d' " inventer " des problèmes : Il y a Prigogine qui oppose ainsi des lois nouvelles, les " lois du chaos ", au déterminisme absolu des lois fondamentales de la physique. La physique est habitée par la passion de la loi, mais la manière dont cette passion est ici réinventée pourrait ouvrir de nouvelles voies, vitales pour une " écologie des pratiques ". Serait-il possible que le physicien ne se présente plus comme celui par qui s'opère la fascinante découverte des lois de la nature? Serait-il possible de célébrer avec lui l'extraordinaire aventure que constitue l'invention d'un objet capable de dicter la manière dont il doit être décrit? (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)

[Time, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe (...) within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless. (shrink)

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.

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)

"This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. (...) To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory's resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism"--. (shrink)

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.

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.

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)

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)

Le prix Nobel de chimie montre comment ses résultats les plus récents en physique théorique lui permettent de résoudre les problèmes qui rendent invraisemblables, malgré leur succès retentissant, tant la physique classique que la mécanique quantique : le paradoxe du temps et le paradoxe quantique. ©Electre 2021.

Contemporary research, across various disciplines, alludes to notion of complexity. Indeed, the phenomenon has even been accredited for comprising a new “world-view” that not only heralds theory construction but also instigates miscellaneous nifty yet practical avenues. On the other hand, however, the complexityparadigm has frequently been criticized of obscurity, contestation and scope imprecision. In addition, its various mutually incommensurable philosophical implications have lead to much heated debates regarding methodological pluralism and metaphorical applications, within literature. To elaborately discussand resolve these concerns, (...) this paper will be organized in three sections: The first section will build on the idiosyncratic characteristics of complexity that differentiate it from related notions of chaos and complicatedness. The second section will shed light on the philosophical deliberations of individual complexityattributes, toward metaphysics of complexity, through elaborately drawn diagrams. Also, this section will draw attention to several conflicting perspectives encompassing the theological, epistemological and ontological domain of complexity. The third section will trace the origins of such paradoxical debates, in the complexity literature, through a ‘Super-System-Outlook’ (SSO) framework. The framework is likely to be of particular significance as it aims to not only divulge an eradicable joint cause of the disparity governing complexity studies but also to propose a possible assimilation of such deliberations. (shrink)

Looks at similarities between Eastern philosophy and Western physics, the connection between cell communicatioin and the immune system, and linguistic properties of the genetic code.

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)