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

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 the system (...) governs or constrains local interactions. This form of downward causation is the key to the DST model of mental causation. In this paper I evaluate the DST approach to mental causation. I will argue that the main problem for current DST approaches to mental causation is that they lack a clear metaphysics. I propose one metaphysical framework (Gillett, 2002a/b/c) that might deal with this deficiency. (shrink)

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove (...) that such a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

Dynamic systems theory is a way of describing the patterns that emerge from relationships in the universe. In the study of interpersonal relationships, within and between species, the scientist is an active and engaged participant in those relationships. Separation between self and other, scientist and subject, runs counter to systems thinking and creates an unnecessary divide between humans and animals.

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 formalism (...) can be applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena. (shrink)

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 caused by other (...) components? Suppose every causal relation requires background conditions, without which it is insufficient. The dynamical system is structured with a tendency to change background conditions for causal relations anytime needed substrates for the pattern's maintenance are missing; under the changed background conditions, alternative causal relations become sufficient to maintain the pattern. The system controls the background conditions under which one or another causal relation can subserve the system's overall pattern, while the components remain causally closed under their given background conditions. (shrink)

Current models of speech motor control rely on either trajectory-based control (DIVA, GEPPETO, ACT) or a dynamical systems approach based on feedback control (Task Dynamics, FACTS). While both approaches have provided insights into the speech motor system, it is difficult to connect these findings across models given the distinct theoretical and computational bases of the two approaches. We propose a new extension of the most widely used dynamical systems approach, Task Dynamics, that incorporates many of the strengths of (...) trajectory-based approaches, providing a way to bridge the theoretical divide between what have been two separate approaches to understanding speech motor control. The Task Dynamics (TD) model posits that speech gestures are governed by point attractor dynamics consistent with a critically damped harmonic oscillator. Kinematic trajectories associated with such gestures should therefore be consistent with a second-order dynamical system, possibly modified by blending with temporally overlapping gestures or altering oscillator parameters. This account of observed kinematics is powerful and theoretically appealing, but may be insufficient to account for deviations from predicted kinematics—i.e., changes produced in response to some external perturbations to the jaw, changes in control during acquisition and development, or effects of word/syllable frequency. Optimization, such as would be needed to minimize articulatory effort, is also incompatible with the current TD model, though the idea that the speech production systems economizes effort has a long history and, importantly, also plays a critical role in current theories of domain-general human motor control. To address these issues, we use Dynamic Movement Primitives (DMPs) to expand a dynamical systems framework for speech motor control to allow modification of kinematic trajectories by incorporating a simple, learnable forcing term into existing point attractor dynamics. We show that integration of DMPs with task-based point-attractor dynamics enhances the potential explanatory power of TD in a number of critical ways, including the ability to account for external forces in planning and optimizing both kinematic and dynamic movement costs. At the same time, this approach preserves the successes of Task Dynamics in handling multi-gesture planning and coordination. (shrink)

From birth to 15 months infants and caregivers form a fundamentally intersubjective, dyadic unit within which the infant’s ability to recognize gender/sex in the world develops. Between about 18 and 36 months the infant accumulates an increasingly clear and subjective sense of self as female or male. We know little about how the precursors to gender/sex identity form during the intersubjective period, nor how they transform into an independent sense of self by 3 years of age. In this Theory and (...) Hypothesis article I offer a general framework for thinking about this problem. I propose that through repetition and patterning, the dyadic interactions in which infants and caregivers engage imbue the infant with an embodied, i.e., sensori-motor understanding of gender/sex. During this developmental period (which I label Phase 1) gender/sex is primarily an intersubjective project. From 15 to 18 months (which I label Phase 2) there are few reports of newly appearing gender/sex behavioral differences, and I hypothesize that this absence reflects a period of developmental instability during which there is a transition from gender/sex as primarily inter-subjective to gender/sex as primarily subjective. Beginning at 18 months (i.e., the start of Phase 3), a toddler’s subjective sense of self as having a gender/sex emerges, and it solidifies by 3 years of age. I propose a dynamic systems perspective to track how infants first assimilate gender/sex information during the intersubjective period (birth to 15 months); then explore what changes might occur during a hypothesized phase transition (15 to 18 months), and finally, review the emergence and initial stabilization of individual subjectivity-the period from 18 to 36 months. The critical questions explored focus on how to model and translate data from very different experimental disciplines, especially neuroscience, physiology, developmental psychology and cognitive development. I close by proposing the formation of a research consortium on gender/sex development during the first 3 years after birth. (shrink)

We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes:i) on one hand the cell proliferation under successive divisions ii) on the other hand, the differentiation between cell lineages. We illustrate this new approach in the case of Caenorhabditis elegans by looking at the (...) early stages of embryogenesis, up to several hundreds of cells (lima bean larval stage). We show how the many results that have been obtained by several groups can be interpreted in terms of values for the parameters controlling the dynamical system. Furthermore, we can extend the model to the cases of genetic mutations. More precisely the teratogenetic and lethal effects are associated with abnormal variation of the control parameters with time. (shrink)

With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, the article sets out how the task demands of system (...) identification and system control can be realised in these environments, and how psychometrically acceptable dependent variables can be derived. (shrink)

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 space description (...) should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed. (shrink)

. 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 networks, logic programs, and evolutionary (...) systems are instances of such interpreted dynamical systems, and thus our results entail that each of them may be described correctly and, in a sense, even completely by qualitative laws that obey the rules of a nonmonotonic logic system. (shrink)

The problem of the direction of time is reconsidered in the light of a generalized version of the theory of abstract deterministic dynamical systems, thanks to which the mathematical model of time can be provided with an internal dynamics, solely depending on its algebraic structure. This result calls for a reinterpretation of the directional properties of physical time, which have been typically understood in a strictly topological sense, as well as for a reexamination of the theoretical meaning of the (...) widespread time-reversal invariance of classical physical processes. (shrink)

Locke & Bogin (L&B) suggest that theoretical principles of ontogenetic development apply to language evolution. If this is the case, then evolutionary theory should utilize epigenetic theories of development to theorize, model, and elucidate the evolution of language wherever possible. In this commentary, I evoke principles of dynamic systems theory to evaluate the evolutionary phenomena presented in the target article.

Neural organization contains a wealth of facts from all areas of brain research and provides a useful overview of physiological data for those working outside the immediate field. Furthermore, it gives a good example that the approach of dynamical system theory together with the concepts of cooperative and competitive interaction can be fruitful for an interdisciplinary approach to cognition.

This article discusses the role of moment-to-moment affect dynamics in mental disorder and aims to integrate recent literature on this topic in the context of complex dynamical system theory. First, we will review the relevance of temporal and contextual aspects of affect dynamics in relation to psychopathology. Related to this, we will discuss recent insights resulting from a network view on affect dynamics in psychopathology. Next, we explore how we can reconcile literature findings from a perspective of complex (...) class='Hi'>dynamical system theory. Finally, future directions with regard to personalized assessment of risk and diagnostic use are discussed. (shrink)

Dynamical systems are mathematical objects meant to formally capture the evolution of deterministic systems. Although no topological constraint is usually imposed on their state spaces, there is prima facie evidence that the topological properties of dynamical systems might naturally depend on their dynamical features. This paper aims to prepare the grounds for a systematic investigation of such dependence, by exploring how the underlying dynamics might naturally induce a corresponding topology.

Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation between these time series when estimating fractal properties. First, we briefly describe how fractal fluctuations have advanced a dynamic system understanding of cognition. Then, we describe mvDFA in detail and highlight some (...) of the advantages of the approach for simulated data. Furthermore, we show how mvDFA can be used to investigate empirical multivariate data using electroencephalographic recordings during a time-estimation task. We discuss this methodological development within the framework of interaction-dominant dynamics. Moreover, we outline how the availability of multivariate analyses can inform theoretical developments in the area of dynamic systems in human behavior. (shrink)

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 on (...) a dynamical landscape of attractors corresponding to the potential eye-movement behaviors of the system. We test three unique predictions of our approach in an empirical study in the VWP, and describe an implementation in an artificial neural network. We discuss the Impulse Processing framework in relation to other models of the VWP. (shrink)

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

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 (...) systems, which I call "cognitive systems". The goal of a cognitive study is to specify a dynamical model of a cognitive system, and then use this model to produce a detailed account of the specific cognitive abilities of that system. The dynamical approach does not limit a-priori the form of the dynamical models which cognitive science may consider. In particular, this approach is compatible with both computational and connectionist modeling, for both computational systems and connectionist networks are special types of dynamical systems. ;To substantiate these methodological claims about cognitive science, I deal first with two questions in two different fields: What is a computational system? What is a dynamical explanation of a deterministic process? ;Intuitively, a computational system is a deterministic system which evolves in discrete time steps, and which can be described in an effective way. In chapter 1, I give a formal definition of this concept which employs the notions of isomorphism between dynamical systems, and of Turing computable function. In chapter 2, I propose a more comprehensive analysis which is based on a natural generalization of the concept of Turing machine. ;The goal of chapter 3 is to develop a theory of the dynamical explanation of a deterministic process. By a "dynamical explanation" I mean the specification of a dynamical model of the system or process which we want to explain. I start from the analysis of a specific type of explanandum--dynamical phenomena--and I then use this analysis to shed light on the general form of a dynamical explanation. Finally, I analyze the structure of those theories which generate explanations of this form, namely dynamical theories. (shrink)

Economic logic impinges on contemporary political theory through both economic reductionism and economic methodology applied to political decision-making (through game theory). The authors argue that the sort of models used are based on mechanistic and linear methodologies that have now been found wanting in physics. They further argue that complexity based self-organization methods are better suited to model the complexities of economy and polity and their interactions with the overall social system.

According to the sensorimotor approach, perception is a form of embodied know-how, constituted by lawful regularities in the sensorimotor flow or in sensorimotor contingencies (SMCs) in an active and situated agent. Despite the attention that this approach has attracted, there have been few attempts to define its core concepts formally. In this paper, we examine the idea of SMCs and argue that its use involves notions that need to be distinguished. We introduce four distinct kinds of SMCs, which we define (...) operationally. These are the notions of sensorimotor environment (open-loop motor-induced sensory variations), sensorimotor habitat (closed-loop sensorimotor trajectories), sensorimotor coordination (reliable sensorimotor patterns playing a functional role), and sensorimotor strategy (normative organization of sensorimotor coordinations). We make use of a minimal dynamical model of visually guided categorization to test the explanatory value of the different kinds of SMCs. Finally, we discuss the impact of our definitions on the conceptual development and empirical as well as model-based testing of the claims of the sensorimotor approach. (shrink)

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability.

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 analysis to (...) describe a graded approach to non-reductive physicalism, and to critically assess Davidson’s arguments for psychological anomaly. I also show how this approach can inform empirical research in cognitive science. (shrink)

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 input (...) to the robot is reconstructed into compositional memory structures through the articulation processes described. (shrink)

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.

Representational drift is a phenomenon of increasing interest in the cognitive and neural sciences. While investigations are ongoing for other sensory cortices, recent research has demonstrated the pervasiveness in which it occurs in the piriform cortex for olfaction. This gradual weakening and shifting of stimulus-responsive cells has critical implications for sensory stimulus–response models and perceptual decision-making. While representational drift may complicate traditional sensory processing models, it could be seen as an advantage in olfaction, as animals live in environments with constantly (...) changing and unpredictable chemical information. Non-topographical encoding in the olfactory system may aid in contextualizing reactions to promiscuous odor stimuli, facilitating adaptive animal behavior and survival. This article suggests that traditional models of stimulus–(neural) response mapping in olfaction may need to be reevaluated and instead motivates the use of dynamical systems theory as a methodology and conceptual framework. (shrink)

Stocks and flows are building blocks of dynamic systems: Stocks change through inflows and outflows, such as our bank balance changing with withdrawals and deposits, or atmospheric CO2 with absorptions and emissions. However, people make systematic errors when trying to infer the behavior of dynamic systems, termed SF failure, whose cognitive explanations are yet unknown. We argue that SF failure appears when people focus on specific system elements, rather than on the system structure and gestalt. Using a standard SF task, (...) SF failure decreased by a global as opposed to local task format; individual global as opposed to local processing styles; and global as opposed to local perceptual priming. These results converge toward local processing as an explanation for SF failure. We discuss theoretical and practical implications on the connections between the scope of attention and understanding of dynamic systems. (shrink)

In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an (...) endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology. (shrink)

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.

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.

Our approach aims at accounting for causal claims in terms of how the physical states of the underlying dynamical system evolve with time. Causal claims assert connections between two sets of physicals states—their truth depends on whether the two sets in question are genuinely connected by time evolution such that physical states from one set evolve with time into the states of the other set. We demonstrate the virtues of our approach by showing how it is able to account (...) for typical causes, causally relevant factors, being ‘the’ cause, and cases of overdetermination and causation by absences. (shrink)

This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with (...) some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science. (shrink)

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 between (...) mind and brain. (shrink)