Search results for 'dynamical systems' (try it on Scholar)

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  1.  75
    Scott Hotton & Jeff Yoshimi (2011). Extending Dynamical Systems Theory to Model Embodied Cognition. Cognitive Science 35 (3):444-479.
    We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this (...)
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  2.  26
    Ichiro Tsuda (2001). Toward an Interpretation of Dynamic Neural Activity in Terms of Chaotic Dynamical Systems. Behavioral and Brain Sciences 24 (5):793-810.
    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 (...)
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  3.  23
    Anuenue Kukona & Whitney Tabor (2011). Impulse Processing: A Dynamical Systems Model of Incremental Eye Movements in the Visual World Paradigm. Cognitive Science 35 (6):1009-1051.
    The Visual World Paradigm (VWP) presents listeners with a challenging problem: They must integrate two disparate signals, the spoken language and the visual context, in support of action (e.g., complex movements of the eyes across a scene). We present Impulse Processing, a dynamical systems approach to incremental eye movements in the visual world that suggests a framework for integrating language, vision, and action generally. Our approach assumes that impulses driven by the language and the visual context impinge minutely (...)
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  4.  2
    Vishnu Sreekumar, Simon Dennis & Isidoros Doxas (2016). The Episodic Nature of Experience: A Dynamical Systems Analysis. Cognitive Science 40 (6):n/a-n/a.
    Context is an important construct in many domains of cognition, including learning, memory, and emotion. We used dynamical systems methods to demonstrate the episodic nature of experience by showing a natural separation between the scales over which within-context and between-context relationships operate. To do this, we represented an individual's emails extending over about 5 years in a high-dimensional semantic space and computed the dimensionalities of the subspaces occupied by these emails. Personal discourse has a two-scaled geometry with smaller (...)
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  5.  39
    Tjeerd Van De Laar (2006). Dynamical Systems Theory as an Approach to Mental Causation. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 37 (2):307-332.
    Dynamical systems theory (DST) is gaining popularity in cognitive science and philosophy of mind. Recently several authors (e.g. J.A.S. Kelso, 1995; A. Juarrero, 1999; F. Varela and E. Thompson, 2001) offered a DST approach to mental causation as an alternative for models of mental causation in the line of Jaegwon Kim (e.g. 1998). They claim that some dynamical systems exhibit a form of global to local determination or downward causation in that the large-scale, global activity of (...)
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  6.  30
    Whitney Tabor, Pyeong W. Cho & Harry Dankowicz (2013). Birth of an Abstraction: A Dynamical Systems Account of the Discovery of an Elsewhere Principle in a Category Learning Task. Cognitive Science 37 (7):1193-1227.
    Human participants and recurrent (“connectionist”) neural networks were both trained on a categorization system abstractly similar to natural language systems involving irregular (“strong”) classes and a default class. Both the humans and the networks exhibited staged learning and a generalization pattern reminiscent of the Elsewhere Condition (Kiparsky, 1973). Previous connectionist accounts of related phenomena have often been vague about the nature of the networks’ encoding systems. We analyzed our network using dynamical systems theory, revealing topological and (...)
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  7.  33
    Harald Atmanspacher (2006). Complementarity in Classical Dynamical Systems. Foundations of Physics 36 (2):291-306.
    The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase (...)
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  8.  48
    Marco Giunti (1992). Computers, Dynamical Systems, Phenomena, and the Mind. Dissertation, Indiana University
    This work addresses a broad range of questions which belong to four fields: computation theory, general philosophy of science, philosophy of cognitive science, and philosophy of mind. Dynamical system theory provides the framework for a unified treatment of these questions. ;The main goal of this dissertation is to propose a new view of the aims and methods of cognitive science--the dynamical approach . According to this view, the object of cognitive science is a particular set of dynamical (...)
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  9. John T. Sanders, Dynamical Systems and Scientific Method.
    Progress in the last few decades in what is widely known as “Chaos Theory” has plainly advanced understanding in the several sciences it has been applied to. But the manner in which such progress has been achieved raises important questions about scientific method and, indeed, about the very objectives and character of science. In this presentation, I hope to engage my audience in a discussion of several of these important new topics.
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  10.  15
    Cliff Hooker (2013). On the Import of Constraints in Complex Dynamical Systems. Foundations of Science 18 (4):757-780.
    Complexity arises from interaction dynamics, but its forms are co-determined by the operative constraints within which the dynamics are expressed. The basic interaction dynamics underlying complex systems is mostly well understood. The formation and operation of constraints is often not, and oftener under appreciated. The attempt to reduce constraints to basic interaction fails in key cases. The overall aim of this paper is to highlight the key role played by constraints in shaping the field of complex systems. Following (...)
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  11.  58
    Marco Giunti (2005). Emulation, Reduction, and Emergence in Dynamical Systems. In Proceedings of the 6th Systems Science European Congress, Paris, September 19-22, 2005. (CD-ROM). AFSCET
    The received view about emergence and reduction is that they are incompatible categories. I argue in this paper that, contrary to the received view, emergence and reduction can hold together. To support this thesis, I focus attention on dynamical systems and, on the basis of a general representation theorem, I argue that, as far as these systems are concerned, the emulation relationship is sufficient for reduction (intuitively, a dynamical system DS1 emulates a second dynamical system (...)
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  12.  30
    Thomas Brihaye (2006). A Note on the Undecidability of the Reachability Problem for o‐Minimal Dynamical Systems. Mathematical Logic Quarterly 52 (2):165-170.
    In this paper we prove that the reachability problem is BSS-undecidable for o-minimal dynamical systems.
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  13.  50
    Marco Van Leeuwen (2005). Questions for the Dynamicist: The Use of Dynamical Systems Theory in the Philosophy of Cognition. [REVIEW] Minds and Machines 15 (3-4):271-333.
    The concepts and powerful mathematical tools of Dynamical Systems Theory (DST) yield illuminating methods of studying cognitive processes, and are even claimed by some to enable us to bridge the notorious explanatory gap separating mind and matter. This article includes an analysis of some of the conceptual and empirical progress Dynamical Systems Theory is claimed to accomodate. While sympathetic to the dynamicist program in principle, this article will attempt to formulate a series of problems the proponents (...)
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  14.  30
    Eric-Jan Wagenmakers, Han L. J. van der Maas & Simon Farrell (2012). Abstract Concepts Require Concrete Models: Why Cognitive Scientists Have Not Yet Embraced Nonlinearly Coupled, Dynamical, Self-Organized Critical, Synergistic, Scale-Free, Exquisitely Context-Sensitive, Interaction-Dominant, Multifractal, Interdependent Brain-Body-Niche Systems. Topics in Cognitive Science 4 (1):87-93.
    After more than 15 years of study, the 1/f noise or complex-systems approach to cognitive science has delivered promises of progress, colorful verbiage, and statistical analyses of phenomena whose relevance for cognition remains unclear. What the complex-systems approach has arguably failed to deliver are concrete insights about how people perceive, think, decide, and act. Without formal models that implement the proposed abstract concepts, the complex-systems approach to cognitive science runs the danger of becoming a philosophical exercise in (...)
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  15. John Collier & Cliff Hooker (1999). Complexly Organised Dynamical Systems. Open Systems and Information Dynamics 6 (3):241–302.
    Both natural and engineered systems are fundamentally dynamical in nature: their defining properties are causal, and their functional capacities are causally grounded. Among dynamical systems, an interesting and important sub-class are those that are autonomous, anticipative and adaptive (AAA). Living systems, intelligent systems, sophisticated robots and social systems belong to this class, and the use of these terms has recently spread rapidly through the scientific literature. Central to understanding these dynamical systems (...)
     
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  16. Charlotte Werndl (2013). Justifying Typicality Measures of Boltzmannian Statistical Mechanics and Dynamical Systems. Studies in History and Philosophy of Science Part B 44 (4):470-479.
    A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. (...)
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  17.  38
    Jeff Yoshimi (2011). Active Internalism and Open Dynamical Systems. Philosophical Psychology 25 (1):1 - 24.
    The question whether cognition is subserved by internal processes in the brain (internalism) or extends in to the world (active externalism) has been vigorously debated in recent years. I show how internalist and externalist ideas can be pursued in a common framework, using (1) open dynamical systems, which allow for separate analysis of an agent's intrinsic and embodied dynamics, and (2) supervenience functions, which can be used to study how low-level dynamical systems give rise to higher-level (...)
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  18.  11
    Marco Giunti (2014). A Representational Approach to Reduction in Dynamical Systems. Erkenntnis 79 (4):943-968.
    According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation is (...)
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  19.  54
    Jeff Yoshimi (2012). Supervenience, Dynamical Systems Theory, and Non-Reductive Physicalism. British Journal for the Philosophy of Science 63 (2):373-398.
    It is often claimed (1) that levels of nature are related by supervenience, and (2) that processes occurring at particular levels of nature should be studied using dynamical systems theory. However, there has been little consideration of how these claims are related. To address the issue, I show how supervenience relations give rise to ‘supervenience functions’, and use these functions to show how dynamical systems at different levels are related to one another. I then use this (...)
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  20.  19
    Joshua Rosaler, Theory Reduction in Physics: A Model-Based, Dynamical Systems Approach.
    In 1973, Nickles identified two senses in which the term `reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in the sciences, and the sense that seeks to extract one physical theory as a mathematical limit of another. These two approaches have since been the focus of most literature on the subject, as evidenced by recent work of Batterman and Butterfield, among others. In this paper, I discuss a third (...)
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  21.  37
    Hannes Leitgeb (2005). Interpreted Dynamical Systems and Qualitative Laws: From Neural Networks to Evolutionary Systems. Synthese 146 (1-2):189 - 202.
    . Interpreted dynamical systems are dynamical systems with an additional interpretation mapping by which propositional formulas are assigned to system states. The dynamics of such systems may be described in terms of qualitative laws for which a satisfaction clause is defined. We show that the systems Cand CL of nonmonotonic logic are adequate with respect to the corresponding description of the classes of interpreted ordered and interpreted hierarchical systems, respectively. Inhibition networks, artificial neural (...)
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  22.  59
    Roman Frigg (2004). In What Sense is the Kolmogorov-Sinai Entropy a Measure for Chaotic Behaviour?—Bridging the Gap Between Dynamical Systems Theory and Communication Theory. British Journal for the Philosophy of Science 55 (3):411 - 434.
    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 (...)
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  23.  49
    W. Schonbein (2005). Cognition and the Power of Continuous Dynamical Systems. Minds and Machines 15 (1):57-71.
    Traditional approaches to modeling cognitive systems are computational, based on utilizing the standard tools and concepts of the theory of computation. More recently, a number of philosophers have argued that cognition is too subtle or complex for these tools to handle. These philosophers propose an alternative based on dynamical systems theory. Proponents of this view characterize dynamical systems as (i) utilizing continuous rather than discrete mathematics, and, as a result, (ii) being computationally more powerful than (...)
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  24.  13
    Arthur B. Markman (2001). Are Dynamical Systems the Answer? Behavioral and Brain Sciences 24 (1):50-51.
    The proposed model is put forward as a template for the dynamical systems approach to embodied cognition. In order to extend this view to cognitive processing in general, however, two limitations must be overcome. First, it must be demonstrated that sensorimotor coordination of the type evident in the A-not-B error is typical of other aspects of cognition. Second, the explanatory utility of dynamical systems models must be clarified.
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  25.  20
    Fred A. Keijzer & Sacha Bem (1996). Behavioral Systems Interpreted as Autonomous Agents and as Coupled Dynamical Systems: A Criticism. Philosophical Psychology 9 (3):323-46.
    Cognitive science's basic premises are under attack. In particular, its focus on internal cognitive processes is a target. Intelligence is increasingly interpreted, not as a matter of reclusive thought, but as successful agent-environment interaction. The critics claim that a major reorientation of the field is necessary. However, this will only occur when there is a distinct alternative conceptual framework to replace the old one. Whether or not a serious alternative is provided is not clear. Among the critics there is some (...)
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  26.  58
    Gerard O’Brien (1998). Digital Computers Versus Dynamical Systems: A Conflation of Distinctions. Behavioral and Brain Sciences 21 (5):648-649.
    The distinction at the heart of van Gelder’s target article is one between digital computers and dynamical systems. But this distinction conflates two more fundamental distinctions in cognitive science that should be keep apart. When this conflation is undone, it becomes apparent that the “computational hypothesis” (CH) is not as dominant in contemporary cognitive science as van Gelder contends; nor has the “dynamical hypothesis” (DH) been neglected.
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  27.  8
    Miklos Redei & Charlotte Werndl, On the History of the Isomorphism Problem of Dynamical Systems with Special Regard to von Neumann's Contribution.
    This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory. In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to Ulam is the very first (...)
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  28.  3
    Jun Tani (1998). An Interpretation of Theself'from the Dynamical Systems Perspective: A Constructivist Approach. Journal of Consciousness Studies 5 (5-6):5-6.
    This study attempts to describe the notion of the ‘self’ using dynamical systems language based on the results of our robot learning experiments. A neural network model consisting of multiple modules is proposed, in which the interactive dynamics between the bottom-up perception and the top-down prediction are investigated. Our experiments with a real mobile robot showed that the incremental learning of the robot switches spontaneously between steady and unsteady phases. In the steady phase, the top-down prediction for the (...)
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  29.  10
    Gyorgy Kampis (1991). Different Forms of Causation in Dynamical Systems: Determinism, Pattern Generation, and Information. World Futures 30 (4):221-237.
    (1991). Different forms of causation in dynamical systems: Determinism, pattern generation, and information. World Futures: Vol. 30, No. 4, pp. 221-237.
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  30.  9
    N. Thomasson & L. Pezard (1999). Dynamical Systems and Depression: A Framework for Theoretical Perspectives. Acta Biotheoretica 47 (3-4):209-218.
    The theory of dynamical systems allows one to describe the change in a system' 's macroscopic behavior as a bifurcation in the underlying dynamics. We show here, from the example of depressive syndrome, the existence of a correspondence between clinical and electro-physiological dimensions and the association between clinical remission and brain dynamics reorganization. On the basis of this experimental study, we discuss the interest of such results concerning the question of normality versus pathology in psychiatry and the relationship (...)
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  31.  32
    Ralph D. Ellis (2005). Generating Predictions From a Dynamical Systems Emotion Theory. Behavioral and Brain Sciences 28 (2):202-203.
    Lewis's dynamical systems emotion theory continues a tradition including Merleau-Ponty, von Bertallanfy, and Aristotle. Understandably for a young theory, Lewis's new predictions do not follow strictly from the theory; thus their failure would not disconfirm the theory, nor their success confirm it – especially given that other self-organizational approaches to emotion (e.g., those of Ellis and of Newton) may not be inconsistent with these same predictions.
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  32.  10
    Clark Glymour, Goethe to Van Gelder: Comments on "Dynamical Systems" Models of Cognition.
    The "dynamical systems" model of cognitive processing is not an alternative computational model. The proposals about "computation" that accompany it are either vacuous or do not distinguish it from a variety of standard computational models. I conclude that the real motivation for van Gelder's version of the account is not technical or computational, but is rather in the spirit of natur-philosophie.
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  33.  30
    Richard Johns (2011). Self-Organisation in Dynamical Systems: A Limiting Result. Synthese 181 (2):255 - 275.
    There is presently considerable interest in the phenomenon of "self-organisation" in dynamical systems. The rough idea of self-organisation is that a structure appears "by itself in a dynamical system, with reasonably high probability, in a reasonably short time, with no help from a special initial state, or interaction with an external system. What is often missed, however, is that the standard evolutionary account of the origin of multi-cellular life fits this definition, so that higher living organisms are (...)
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  34.  11
    W. -H. Steeb, M. Kloke, B. M. Spieker & A. Kunick (1985). Integrability of Dynamical Systems and the Singular-Point Analysis. Foundations of Physics 15 (6):637-666.
    Various aspects of the integrability of dynamical systems are discussed with the help of the singular point analysis. In particular the connection with the Painlevé property is described. Several examples will serve as illustrations.
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  35.  25
    David Spurrett (2002). Information Processing and Dynamical Systems Approaches Are Complementary. Behavioral and Brain Sciences 25 (5):639-640.
    Shanker & King (S&K) trumpet the adoption of a “new paradigm” in communication studies, exemplified by ape language research. Though cautiously sympathetic, I maintain that their argument relies on a false dichotomy between “information” and “dynamical systems” theory, and that the resulting confusion prevents them from recognizing the main chance their line of thinking suggests.
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  36.  24
    Jun Tani (2004). The Dynamical Systems Accounts for Phenomenology of Immanent Time: An Interpretation by Revisiting a Robotics Synthetic Study. Journal of Consciousness Studies 11 (9):5-24.
    This paper discusses possible correspondences between the dynamical systems characteristics observed in our previously proposed cognitive model and phenomenological accounts of immanent time considered by Edmund Husserl. Our simulation experiments in the anticiparatory learning of a robot showed that encountering sensory-motor flow can be learned as segmented into chunks of reusable primitives with accompanying dynamic shifting between coherences and incoherences in local modules. It is considered that the sense of objective time might appear when the continuous sensory-motor flow (...)
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  37.  5
    D. Lynn Holt & R. Glynn Holt (1993). Regularity in Nonlinear Dynamical Systems. British Journal for the Philosophy of Science 44 (4):711-727.
    Laws of nature have been traditionally thought to express regularities in the systems which they describe, and, via their expression of regularities, to allow us to explain and predict the behavior of these systems. Using the driven simple pendulum as a paradigm, we identify three senses that regularity might have in connection with nonlinear dynamical systems: periodicity, uniqueness, and perturbative stability. Such systems are always regular only in the second of these senses, and that sense (...)
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  38.  18
    Frank van der Velde & Marc de Kamps (1998). Toward a Synthesis of Dynamical Systems and Classical Computation. Behavioral and Brain Sciences 21 (5):652-653.
    Cognitive agents are dynamical systems but not quantitative dynamical systems. Quantitative systems are forms of analogue computation, which is physically too unreliable as a basis for cognition. Instead, cognitive agents are dynamical systems that implement discrete forms of computation. Only such a synthesis of discrete computation and dynamical systems can provide the mathematical basis for modeling cognitive behavior.
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  39.  15
    Herbert Jaeger (1998). Today's Dynamical Systems Are Too Simple. Behavioral and Brain Sciences 21 (5):643-644.
    Cognitive systems are wilder than today's dynamical systems theory can handle. Cognitive systems might be tamed in principle, but the very notion of a dynamical system will change in the process.
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  40. Ralph D. Ellis (2001). Can Dynamical Systems Explain Mental Causation? Journal of Mind and Behavior 22 (3):311-334.
    Dynamical systems promise to elucidate a notion of top–down causation without violating the causal closure of physical events. This approach is particularly useful for the problem of mental causation. Since dynamical systems seek out, appropriate, and replace physical substrata needed to continue their structural pattern, the system is autonomous with respect to its components, yet the components constitute closed causal chains. But how can systems have causal power over their substrates, if each component is sufficiently (...)
     
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  41. John Collier, Functionality and Autonomy in Open Dynamical Systems.
    In Robert West’s talk last week, dynamical systems theory (DST) was applied to a specific problem involving interacting symbolic systems, without much reference to how those systems are embodied or related to other types of systems. Despite this level of abstraction, DST can yield interesting results, though one might be left wondering if it really leads to understanding, or what it all means. In particular, Robert noted problems he has in convincing referees that the sort (...)
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  42.  3
    Douglas T. Kenrick, Norman Li & Jonathan E. Butner (2000). Dynamical Systems and Mating Decision Rules. Behavioral and Brain Sciences 23 (4):607-608.
    Dynamical simulations of male and female mating strategies illustrate how traits such as restrictedness constrain, and are constrained by, local ecology. Such traits cannot be defined solely by genotype or by phenotype, but are better considered as decision rules gauged to ecological inputs. Gangestad & Simpson's work draws attention to the need for additional bridges between evolutionary psychology and dynamical systems theory.
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  43.  6
    Wassim M. Haddad, VijaySekhar Chellaboina & Sergey G. Nersesov (2006). Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control. Princeton University Press.
    This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems.
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  44. P. Van Geert (2009). Nonlinear Complex Dynamical Systems in Developmental Psychology. In Stephen J. Guastello, Matthijs Koopmans & David Pincus (eds.), Chaos and Complexity in Psychology: The Theory of Nonlinear Dynamical Systems. Cambridge University Press
  45.  8
    Cliff Hooker, Conceptualising Reduction, Emergence and Self-Organisation in Complex Dynamical Systems.
    This chapter describes the application of reduction concepts in emergence and self organization of complex dynamical system. Condition-dependent laws compress and dynamical equation sets provide implicit compressed representations even when most of that information is not explicitly available without decompression. And, paradoxically, there is still the determined march of fundamental analytical dynamics expanding its compression reach toward a Theory of Everything—even while the more rapidly expanding domain of complex systems dynamics confronts its assumptions and its monolithicity. Nor (...)
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  46.  16
    Cliff A. Hooker (1997). Dynamical Systems in Development: Review Essay of Linda V. Smith & Esther Thelen (Eds) a Dynamics Systems Approach to Development: Applications. Philosophical Psychology 10 (1):103 – 112.
    This book focuses on showing how the ideas central to the new wave oj dynamic systems studies may also form the basis for a new and distinctive theory of human development where both global order and local variability in behaviour emerge together from the same organising dynamical interactions. This also sharpens our understanding of the weaknesses of the traditional formal, structuralist theories. Conversely, dynamical models have their own matching set of problems, many of which are consiously explored (...)
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  47.  48
    Noboru Watanabe (2011). Note on Entropies of Quantum Dynamical Systems. Foundations of Physics 41 (3):549-563.
    We review some techniques and notions for quantum information theory. It is shown that the dynamical entropies is discussed and some numerical computations of these entropies are carried for several states.
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  48.  12
    James L. McClelland, Matthew M. Botvinick, David C. Noelle, David C. Plaut, Timothy T. Rogers, Mark S. Seidenberg & Linda B. Smith (2010). Letting Structure Emerge: Connectionist and Dynamical Systems Approaches to Cognition. Trends in Cognitive Sciences 14 (8):348-356.
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  49. Stephen J. Guastello & R. A. M. Gregson (eds.) (2011). Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data. Crc Press.
  50.  10
    Stephen H. Kellert & Lawrence Sklar (1997). In the Wake of Chaos: Unpredictable Order in Dynamical Systems. Philosophy of Science 64 (1):181.
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