Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems

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.     

Social dynamics in the preschool

In this paper, we consider how concepts from dynamic systems (such as attractors, repellors, and self-organization) can be applied to the study of young children’s peer relationships. We also consider how these concepts can be used to explore basic issues involving early peer processes. We use the dynamical systems approach called state space grid (SSG) analysis and consider how it can be expanded beyond the study of dyads to the study of larger social groups and networks. In particular, we explore the role of homophily—that is, behavioral and sex similarity—as factors in the self-organization of young children’s social groups. A dynamic systems approach allows for consideration of peer processes difficult to assess using more traditional approaches.     

A comparison of information processing and dynamical systems perspectives on problem solving

Abstract

This article compares the information processing and dynamical systems perspectives on problem solving. Key theoretical constructs of the information-processing perspective include “searching” a “problem space” by using “heuristics” that produce “incremental” changes such as reaching a “subgoal” to solve a puzzle. Key theoretical constructs of the dynamical-systems perspective include “positive attractors”, “negative attractors”, and “latent attractors” that can cause large “nonincremental” changes in the possibility of a solution through the “emergence” of new ideas and beliefs that can resolve a conflict. The proposed alignment maps dynamical-system constructs to information-processing constructs: state space to problem space, negative attractor to impasse, positive attractor to productive subgoal, latent attractor to implicit cognition, and nonincremental change to insight. The purpose of the mapping is to explore similarities and differences between these constructs. Research from cognitive and social psychology illustrates how using constructs from both perspectives is helpful. The concluding section on Future Directions recommends an agenda based on three objectives: (1) create ontologies to organise current knowledge, (2) conduct research to obtain new knowledge, and (3) provide education to inform students about this knowledge.     

Rigidity in Parent—Child Interactions and the Development of Externalizing and Internalizing Behavior in Early Childhood

Behavioral rigidity is a common feature of many psychopathologies, yet the association between rigidity and the development of childhood psychopathology has not been studied. State space grids (a dynamic systems [DS] method) were used to examine the relation between rigidity in parent-child interactions and childhood externalizing and internalizing problems. High-risk kindergarten children (n = 240) and their parents were observed for 2 hr engaging in a variety of tasks that were expected to elicit a range of affect. State space grid analysis of the observational data revealed an association between rigidity in parent-child interactions and child externalizing behavior problems in the fall and spring of kindergarten and 1st grade, and with growth in those problems over time. Rigidity was associated with concurrent levels and with chronic high-level internalizing problems. Strengths and limitations of the new DS methodology in relation to understanding child psychopathology are discussed.     

Multiple Points of Intervention as an Approach in Child Psychotherapy

ABSTRACT

This article develops an integrated model that emphasizes multiple points of intervention in therapeutic work with children. It draws on nonlinear dynamic systems theory, Winnicott's theory of play and transitional space, elements of contemporary relational theory, client-centered therapy, Gestalt therapy, family systems, behavior therapy, selected aspects of cognitive behavior therapy, psychological education, and school consultations.     

The Mind's Multiplicity and Continuity

The article opens with a fairly detailed overview of the research on nonlinear dynamic systems, deterministic chaos, and complexity theory—referred to collectively as complexity theory. The second part of the article is aimed at applying this research to an interesting discussion that has developed in the psychoanalytic literature regarding the fundamental nature of the self as either singular or multiple. Chaotic systems (a class of nonlinear systems) exhibit staggering variability, sensitivity, and adaptation in response to perturbation (in the form of sensitive dependence on initial conditions), while also demonstrating an enduring and distinctive coherence and continuity in their overall organization (in the form of strange attractors). As such, chaotic systems are useful in conceptualizing how relatively healthy people remain recognizable (or in character) in the midst of their variability, multiplicity, and change. By contrast, pathology of the self from the perspective of nonlinear dynamic systems is characterized by the repetitive, periodic and self-same quality of mental states.     

Mechanics of the animate.

Behavior is treated as basic physics. Dimensions are identified and their transformations from physical specification to axes in behavioral space are suggested. Responses are treated as action patterns arrayed along a continuum of activation energy. Behavior is seen as movement along a trajectory through this behavior space. Incentives or reinforcers are attractors in behavior space, at the centers of basins of lowered potential. Trajectories impinging on such basins may be captured; repeated capture will warp the trajectory toward a geodesic, a process called conditioning. Conditioning is enhanced by contiguity, the proximity between the measured behavior and the incentive at the end of the trajectory, and by contingency, the depth of the trajectory below the average level of the potential energy landscape. Motivation is seen as the potential of an organism for motion under the forces impinging on it. Degree of motivation is characterized by the depth of the potential field, with low motivation corresponding to a flat field and a flat gradient of activation energy. Drives are the forces of incentives propagated through behavior space. Different laws for the attenuation of drive with behavioral distance are discussed, as is the dynamics of action. The basic postulate of behavior mechanics is incentive-tracking in behavior space, the energy for which is provided by decreases in potential. The relation of temporal gradients to response differentiation and temporal discrimination is analyzed. Various two-body problems are sketched to illustrate the application of these ideas to association, choice, scalar timing, self-control, and freedom.     

Motivational systems of agonistic behavior in muroid rodents: A comparative review and neural model

The data on agonistic behavior of muroid rodents that have been obtained from field observations and laboratory experiments are reviewed and compared in terms of a hypothetical model of the neural organization of these behaviors. The neural model has been presented elsewhere and is used here only as a way to organize the data. The data are organized in terms of four hypothetical motivational systems: Offense, defense, submission, and patrol/marking. The various behaviors are considered as motor patterns and are compared and analyzed in terms of the proposed motivating, releasing, and directing stimuli of the motivational systems. Interactions and overlaps between the motivational systems are also considered. It is concluded that the organization of agonistic behavior may be similar across all species of muroid rodents. Generalizations are complicated by the profound effects of ontogenetic factors. Four categories of behaviors differ from species to species: Scent-marking, submissive behaviors, threat behaviors, and alarm signals. The possible phylogenetic and ontogenetic factors in these differences are considered.     

A graphical method to aid the sequential analysis of observational data

In this paper, two methods of sequential analysis are applied to hypothetical observational data. The first method employs the conventional “conditional probability” approach, illustrated using the GSEQ program (Bakeman & Quera, 1995). In order to overcome some of the difficulties associated with the conditional probability approach, the second method employs a new “normalized and pooled” approach. Essentially, by normalizing periods of time preceding, during, and following each occurrence of a nominated “given” behavior, the proportion of time units devoted to a “target” behavior can be estimated and then pooled across all occurrences of the given behavior. A summary diagram representing the likelihood that the target behavior precedes, occurs concurrently with, and follows the given behavior can then be constructed. Elements of this summary diagram can also be quantified. Given the graphical nature of the output, and its ease of use, the normalized and pooled approach may help to promote the use of sequential analysis in applied settings.     

道德动机动态系统理论：一种道德发展的新科尔伯格取向

在科尔伯格道德认知发展阶段理论、动态系统理论和自我决定理论基础上,Kaplan提出了道德动机的动态系统理论,把道德动机界定为认知和情绪成分自我组织和自我调节的动态发展过程。该理论有其特定的提出背景、基本观点和主要内容,并且具有一定的实证证据支持。未来研究应着力解决道德认知与情绪的关系、环境因素的影响、横断研究与纵向研究的结合以及研究工具的完善等问题。     

Applying Chaos Theory to Careers: Attraction and attractors

This article presents the Chaos Theory of Careers with particular reference to the concepts of “attraction” and “attractors”. Attractors are defined in terms of characteristic trajectories, feedback mechanisms, end states, ordered boundedness, reality visions and equilibrium and fluctuation. The identified types of attractors (point, pendulum, torus and strange) and their relevance to career development are described. The attractor concept is then applied to major barriers in career development and life transition by a consideration of closed and open systems thinking. It is contended that ultimately the context of human experience is an open system and that career development difficulties arise when closed systems thinking is used in an open systems reality. The practical counseling applications and counseling research evidence using attractors are briefly reviewed. The additional potential contributions of the Chaos Theory of Careers to the career development field are also outlined.     

Interpersonal Pattern Dynamics and Adaptive Behavior in Multiagent Neurobiological Systems: Conceptual Model and Data

ABSTRACT

Ecological dynamics characterizes adaptive behavior as an emergent, self-organizing property of interpersonal interactions in complex social systems. The authors conceptualize and investigate constraints on dynamics of decisions and actions in the multiagent system of team sports. They studied coadaptive interpersonal dynamics in rugby union to model potential control parameter and collective variable relations in attacker–defender dyads. A videogrammetry analysis revealed how some agents generated fluctuations by adapting displacement velocity to create phase transitions and destabilize dyadic subsystems near the try line. Agent interpersonal dynamics exhibited characteristics of chaotic attractors and informational constraints of rugby union boxed dyadic systems into a low dimensional attractor. Data suggests that decisions and actions of agents in sports teams may be characterized as emergent, self-organizing properties, governed by laws of dynamical systems at the ecological scale. Further research needs to generalize this conceptual model of adaptive behavior in performance to other multiagent populations.     

Mathematical models in Newton's Principia: A new view of the ‘Newtonian Style’

In this essay I argue against I. Bernard Cohen's influential account of Newton's methodology in the Principia: the ‘Newtonian Style’. The crux of Cohen's account is the successive adaptation of ‘mental constructs’ through comparisons with nature. In Cohen's view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical‐deductive, which is at odds with Newton's rejection of the hypothetical‐deductive method. An adequate account of Newton's methodology needs to show how Newton's method proceeds differently from the hypothetical‐deductive method. In the constructive part I argue for my own account, which is model based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton's models is a result of exploring increasingly complex force functions (intra‐theoretical dynamics) rather than a successive comparison with nature (extra‐theoretical dynamics). Nature did not enter the scene here. This intra‐theoretical dynamics is related to the ‘autonomy of the models’.     

Equilibria in Personality States: A Conceptual Primer for Dynamics in Personality States

We provide a basic, step-by-step introduction to the core concepts and mathematical fundamentals of dynamic systems modelling through applying the Change as Outcome model, a simple dynamical systems model, to personality state data. This model characterizes changes in personality states with respect to equilibrium points, estimating attractors and their strength in time series data. Using data from the Personality and Interpersonal Roles study, we find that mean state is highly correlated with attractor position but weakly correlated with attractor strength, suggesting strength provides added information not captured by summaries of the distribution. We then discuss how taking a dynamic systems approach to personality states also entails a theoretical shift. Instead of emphasizing partitioning trait and state variance, dynamic systems analyses of personality states emphasize characterizing patterns generated by mutual, ongoing interactions. Change as Outcome modelling also allows for estimating nuanced effects of personality development after significant life changes, separating effects on characteristic states after the significant change and how strongly she or he is drawn towards those states (an aspect of resiliency). Estimating this model demonstrates core dynamics principles and provides quantitative grounding for measures of ‘repulsive’ personality states and ‘ambivert’ personality structures. © 2020 European Association of Personality Psychology     

Robustness to temporal constraint explains expertise in ball-over-net sports

The present study investigated motor expertise in interpersonal competitive ball-over-net sports in terms of a dynamical system with temporal input. In a theoretical framework, the behavior of the system is characterized by a fractal-like structure according to switching input, which changes uniquely according to the duration of input and internal parameter of the system. We investigated periodic movements, in which the player executed a forehand or backhand stroke repeatedly, and continuous switching movements, in which the player continuously switched between two movement patterns corresponding to hitting the ball under two ball directions and with six temporal constraint conditions during a table tennis rally. In the periodic movement, we observed two limit-cycle attractors corresponding to each direction in the phase space independent of temporal constraint or skill level. Conversely, in the continuous switching movement, a transition in trajectories between the two limit-cycle attractors was observed in the phase space, and this transition was characterized by a fractal-like structure. The fractal-like structure moved closer to the random structure as temporal constraint increased independent of skill level. However, the temporal constraint condition closest to the random structure was higher for the advanced players than for the novices, indicating that robustness to the temporal constraint was higher for the advanced players than for the novices. Our results suggest that motor expertise in interpersonal competitive ball-over-net sports is more robust to temporal constraints with various inputs.     

The dynamics of perception and action

How might one account for the organization in behavior without attributing it to an internal control structure? The present article develops a theoretical framework called behavioral dynamics that integrates an information-based approach to perception with a dynamical systems approach to action. For a given task, the agent and its environment are treated as a pair of dynamical systems that are coupled mechanically and informationally. Their interactions give rise to the behavioral dynamics, a vector field with attractors that correspond to stable task solutions, repellers that correspond to avoided states, and bifurcations that correspond to behavioral transitions. The framework is used to develop theories of several tasks in which a human agent interacts with the physical environment, including bouncing a ball on a racquet, balancing an object, braking a vehicle, and guiding locomotion. Stable, adaptive behavior emerges from the dynamics of the interaction between a structured environment and an agent with simple control laws, under physical and informational constraints.     

Timing, clocks, and dynamical systems.

Theoretical and experimental issues for our understanding of the timing of motor acts are reviewed, contrasting stochastic and dynamic timing models. It is argued that the theory of dynamical systems and, in particular, of limit cycle attractors, provides a unified framework within which these issues can be appreciated. The strength of stochastic timing models in the domain of absolute timing is contrasted with the strength of dynamic timing models in the domain of relative timing, the unification of the two domains being currently under way. It is further argued that accounts of timing must examine the interrelation between timing and other levels of processing involved in movement generation, in particular, the representation of spatial aspects of movement and the control of movement. The emergence of discrete event structure in timing skills is discussed from a dynamical systems perspective. Finally, the understanding of the timing structure of discrete movement is raised as a further challenge for future work.     

Logic programs, iterated function systems, and recurrent radial basis function networks

Graphs of the single-step operator for first-order logic programs—displayed in the real plane—exhibit self-similar structures known from topological dynamics, i.e., they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which approximate logic programs in the presence of function symbols.     

theorizing non-linear communities: on social deviance and housing the homeless

Theories of deviance abound; however, little attention has been given to the construction and meaning of deviance in postmodern society. According to some theorists, one conceptual variant of postmodernism is chaology or non-linear dynamical systems theory. In this article, the relevance of chaos theory for advancing our understanding of social deviance is examined. In particular, such notions as non-linearity, fractal space, attractors, self-similarity, bifurcations, and dissipative structures are described as constitutive of the postmodern agenda. These insights are then applied to the difficult and complex issue of housing the homeless, especially shelter strategies designed to create personhood and place for the poor and disenfranchised.