Showing papers in "Nonlinear Dynamics, Psychology, and Life Sciences in 2002"
TL;DR: In this article, the authors report the results of one subject's performance in a challenging search task in which 10,215 fixations were accumulated, and a number of statistical and spectral tests revealed both fractal and 1/f structure.
Abstract: The ubiquity of apparently random behavior in visual search (e.g., Horowitz & Wolfe, 1998) has led to our proposal that the human oculomotor system has subtle deterministic properties that underlie its complex behavior. We report the results of one subject's performance in a challenging search task in which 10,215 fixations were accumulated. A number of statistical and spectral tests revealed both fractal and 1/f structure. First, scaling properties emerged in differences across eye positions and their relative dispersion (SD/M)—both decreasing over time. Fractal microstructure also emerged in an iterated function systems test and delay plot. Power spectra obtained from the Fourier analysis of fixations produced brown (1/f2) noise and the spectra of differences across eye positions showed 1/f (pink) noise. Thus, while the sequence of absolute eye positions resembles a random walk, the differences in fixations reflect a longer-term dynamic of 1/f pink noise. These results suggest that memory across eye-movements may serve to facilitate our ability to select out useful information from the environment. The 1/f patterns in relative eye positions together with models of complex systems (e.g., Bak, Tang & Wiesenfeld, 1987) suggest that our oculomotor system may produce a complex and self-organizing search pattern providing maximum coverage with minimal effort.
103 citations
TL;DR: In this paper, a theory of emergence based on a clarification and new interpretation of the singular nature of emergent levels is proposed, which is linked to the idea of logical depth as a complexity measure.
Abstract: Suggestions are offered for a theory of emergence based on a clarification and new interpretation of the singular nature of emergent levels. These suggestions cover formalisms, formulations, and measurements. In contrast to mere collectivities, as well as the rendering of macro- and micro-levels in entropy formulations, order parameters, and distinctions in temporal dynamics, emergent levels are described as “privileged” and “confounded.” A discussion of the insufficiency of previous formalisms in dealing with the structural novelty of emergent levels sets the stage for the introduction of a new formal construct, that of self-transcending constructions. This construct is linked to the idea of logical depth as a complexity measure. The advantages of a semantic rather than information–theoretic perspective are discussed. In addition, the tendency to confuse levels in models with levels in emergent phenomena themselves is described. Finally, conclusions about emergent levels as a new natural kind construct are offered.
36 citations
TL;DR: In this paper, the authors discuss the importance of the theory of complex systems for analyzing economic evolution and emphasize the necessity of the structural dynamic approach and discuss possible implications of the theories for studying economic processes with different speeds of change.
Abstract: The purpose of this paper is to discuss the significance of the theory of complex systems for analyzing economic evolution. We emphasize the necessity of the structural dynamic approach and discuss possible implications of the theory of complex systems for studying economic processes with different speeds of change. We illustrate a way to construct a general economic theory that includes the main economic theories of competition with government intervention as special cases in the structural sense.
25 citations
TL;DR: In this article, the dynamics of collective decision when an individual adapts his rational decision to the others' is studied, and the roles of particular types of agents such as hardcore, conformists, and nonconformists are investigated.
Abstract: This paper is about the dynamics of collective decision when an individual adapts his rational decision to the others' We consider an organization of heterogeneous agents, in which each agent faces the binary decision problem The standard way of modeling a collective decision is to assume everyone has the same value or payoff structure This paper considers collective decision of agents with heterogeneous payoffs We obtain and classify rational decision rules of heterogeneous agents into a few categories depending on their idiosyncratic payoff structure We also obtain the micro–macro dynamics that relate the aggregate collective decision with the underlying individual decisions We investigate the roles of particular types of agents such as hardcore, conformists, and nonconformists We show that agents' rational behavior combined with the others produce stable orders, and sometimes complex cyclic behavior
22 citations
TL;DR: In this paper, the mouse paradigm was used to assess near-instantaneous changes in affect over a short time and the instantaneous data yielded a summary measure of mean affect, as well as indices of variability.
Abstract: How are momentary microscopic assessments of behavioral dynamics related to traditional macroscopic, static measures? The present study used the computerized “mouse paradigm” to assess near-instantaneous changes in affect over a short time. Dynamic indices were computed from approximately 1400 measurements from the last 2.5 minutes of a 3-minute assessment. Subjects monitored and reported emotional states by moving a cursor along a dimension from “Sadder” to “Happier.” They also completed self-report measures: Scales 2 (Depression) and 9 (Mania) of the MMPI-2, the Positive and Negative Affect Scale, and the Wisconsin scales of Physical Anhedonia and Hypomanic traits. The instantaneous data yielded a summary measure of mean affect, as well as indices of variability. Complexity indices were derived and examined. Mean affect ratings correlated in expected directions with the paper and pencil measures. There was evidence for low-dimensional chaos in short-term affect dynamics. As hypothesized, greater complexity was associated with Pleasant Affect and Hypomania but was negatively correlated with Anhedonia.
22 citations
TL;DR: This paper argues that dream experiences owe both their structure and meaning to stochastic self-organizing properties of the brain during sleep, and this conception of dreaming offers a common meeting ground for brain-based studies of dreaming and psychological dream theory.
Abstract: This paper argues that dream experiences owe both their structure and meaning to stochastic self-organizing properties of the brain during sleep. Several lines of evidence support the notion that the dreaming brain can be understood as a process system that exhibits chaos-like stochastic properties that are highly sensitive to internal influences. This sensitivity is due, first, to the fact that the dreaming brain gates out external input, thus operating without the stabilizing influences of waking feedback. Second, the pre-frontal cortex in both REM and non-REM (NREM) sleep is only minimally activated, thus the brain operates with weakened volition, reduced logic, and diminished self-reflection. Third, there is a reduction of neuromodulatory inhibition during sleep, which is most pronounced during REM sleep, allowing the brain to respond to minute internal stimulation. Finally, the REM sleeping brain is subject to powerful intermittent cholinergic PGO activity that may provide vigorous stimulation for complex dream activity. Taken in overview, this conception of dreaming offers a common meeting ground for brain-based studies of dreaming and psychological dream theory.
21 citations
TL;DR: In this article, a phase-randomized surrogate time series is used as a control to overcome the nonlinear determinism of the chaotic Henon attractor, and participants viewed the previous eight days temperatures and then predicted temperatures for the next four days, over 120 trials.
Abstract: Previous studies suggesting that people predict chaotic sequences better than chance have not discriminated between sensitivity to nonlinear determinism and facilitation using autocorrelation. Since prediction accuracy declines with increases in the look-ahead window in both cases, a decline in prediction accuracy does not imply chaos sensitivity. To overcome this problem, phase-randomized surrogate time series are used as a control. Such series have the same linear properties as the original chaotic sequence but contain no nonlinear determinism, i.e. chaos. In the experimental task, using a chaotic Henon attractor, participants viewed the previous eight days temperatures and then predicted temperatures for the next four days, over 120 trials. The control group experienced a sample from a corresponding phase-randomized surrogate series. Both time series were linearly transformed to provide a realistic temperature range. A transformation of the correlation between observed and predicted values decreased over days for the chaotic time series, but remained constant and high for the surrogate series. The interaction between the days and series factors was statistically significant, suggesting that people are sensitive to chaos, even when the autocorrelation functions and power spectra of the control and experimental series are identical. Implications for the psychological assessment of individual differences in human prediction are discussed.
20 citations
TL;DR: In this article, the authors studied how long-term swings and short-term stock price volatility in the U.S. auto industry are related to innovative efforts and switching of market shares of firms.
Abstract: The currently ongoing IT-revolution is a great challenge for economists. The industry displays ever arising new technologies, unstable market shares, long-term swings, and short-term volatility of stock prices. Yet, to study those phenomena empirically one is constrained by a lack of data. The U.S. auto industry, for which long-term time series are available, has shared a similar experience since its early development. This paper studies how long-term swings and short-term stock price volatility in the U.S. auto industry is related to innovative efforts and switching of market shares of firms. The early period of the life-cycle of the industry was characterized by high product innovation, high market share instability, volatile stock prices, and the later period by fewer firms, process innovation, more stable market shares and less stock price volatility. In this paper we focus on the “transition” period leading from the first to the second period and study the relation of innovative effort, market share fluctuations and stock price dynamics. After presenting stylized facts on the life-cycle of the industry we introduce a dynamic model that is able to replicate some of the stylized facts. The dynamic model admits heterogeneous firms and encompasses both evolutionary as well as optimizing approaches.
13 citations
TL;DR: In this paper, the control problem of the equilibrium state of the prey-predator model has been studied and the optimal control law is derived from the conditions that ensure the asymptotic stability of this model using the Lyapunov function.
Abstract: The control problem of the equilibrium state of prey-predator model has been studied. The equilibrium states of prey-predator model are found. The optimal control law is derived from the conditions that ensure the asymptotic stability of the equilibrium state of this model using the Lyapunov function. The general solution of the equations of the perturbed state as a function of time is obtained. Graphical and numerical simulation studies of the obtained results are presented.
12 citations
TL;DR: In this paper, a case study of a 48-hour cyclic manicdepressive patient was presented, which further demonstrates the association between nonlinear EEG characteristics and mood variations as previously reported by Thomasson et al.
Abstract: This research report presents the case study of a 48-hour cyclic manicdepressive patient which further demonstrates the association between nonlinear EEG characteristics and mood variations as previously reported by Thomasson et al. (2000). The evolution of brain dynamics and mood were daily measured during a week. Global complexity of brain electrical activity was estimated by a nonlinear index (entropy) and mood modulations were evaluated by a clinical self-assessment scale (BfS'). Illustrating the concept of “dynamical disease,” a significant co-variation between the nonlinear EEG index and mood evolution (Spearman correlation coefficient ρ = 0.92, p = .008) was observed. This result strengthens the previous ones and demonstrates a clear association between nonlinear brain dynamics and state of mind in psychopathology.
11 citations
TL;DR: This paper argues for the central role of “Somewhat complicated” nonlinear dynamical systems in modeling both positive psychology and physical health, and proposes that the good life emerges from systems composed of coupled modular components, potentially capable of chaotic behavior.
Abstract: Health has historically eluded consistent definition and baffled people's attempts at self-improvement. This paper argues for the central role of “Somewhat complicated” nonlinear dynamical systems in modeling both positive psychology and physical health. Whether personal attributes or behaviors are salutogenic or harmful is dependent on context and intensity. In addition, people simultaneously and relatively independently seek sometimes-contradictory outcomes. This establishes the place of intrapsychic conflict in health. The paper proposes that the good life emerges from systems composed of coupled modular components, potentially capable of chaotic behavior. Positive psychology and healthy physiology derive from linked regulative systems that are relatively loosely-coupled, distributed, and that rely on heuristic processes rather than algorithms guaranteeing solution to pursue well-being. The adoption of these “Somewhat complicated” models does not require theories of health to be intricate, nor to employ mechanisms with fractal structure; complex function can emerge from simple systems. Potentially healthy systems attributes are addressed, including current interest in “healthy chaos,” and an illustrative model is developed.
TL;DR: In this article, the authors argue that attempts at controlling problematic thoughts, emotions, or behaviors can lead to nonlinearity in mental/behavioral dynamics and illustrate their model by fitting threshold autoregression models to self-recorded time series of the daily highs in intensity of anxiety and obsessive ruminations, kept by an individual in therapy for this problem.
Abstract: In recent years there has been considerable interest in the construction of nonlinear models of the dynamics of human behavior In this exploratory article we argue that attempts at controlling problematic thoughts, emotions, or behaviors can lead to nonlinearity in mental/behavioral dynamics We illustrate our model by fitting threshold autoregression models to self-recorded time series of the daily highs in intensity of anxiety and obsessive ruminations, kept by an individual in therapy for this problem In our discussion, we raise the possibility that bifurcations that occur in this nonlinear model may offer insight into mental control paradoxes
TL;DR: The model presented here studied a role of parameters related to a flow of resource through the agents of a population and individual sociability appeared to be a key parameter in the self-organization of the population.
Abstract: Two versions of a model, named Resource, were developed within the Ensembles with Variable Structure (EVS) approach The EVS-approach represents interacting groups (populations) with a flexible structure of connections and a diversity of elements (agents), where agents possess an abstract set of characteristics, and seek to form connections with other agents according to the degree of compatibility between these characteristics The model presented here studied a role of parameters related to a flow of resource through the agents of a population Individual sociability appeared to be a key parameter in the self-organization of the population The percentage of an individual resource that an agent is allowed to spend was also an important resource-related parameter Some other phenomena are reported as well
TL;DR: In this paper, the authors propose an agent model of financial markets and analyzes factors leading to speculative bubbles and speculative chaos of the asset price, and show that the nonlinearity of the excess demand functions, which are derived as a result of the traders' utility maximization, might generate speculative bubbles.
Abstract: This paper proposes an agent model of financial markets and analyzes factors leading to speculative bubbles and speculative chaos of the asset price. A financial market is thought to contain two typical types of traders: fundamentalists and chartists who try to maximize their utility. It is shown that the nonlinearity of the excess demand functions, which are derived as a result of the traders' utility maximization, might generate speculative bubbles and speculative chaos of the asset price.
TL;DR: In this paper, the authors considered the possibility of complex dynamics in fishery systems, both of the chaotic and catastrophic variety, and policy responses to these problems are seen to involve the precautionary principle to mitigate the threat of catastrophic discontinuities and the scale-matching principle to ensure that management and property rights system are properly implemented.
Abstract: Fishery dynamics are considered within the context of an integrated ecologic–economic, or bioeconomic, approach. The possibility of complex dynamics is examined, both of the chaotic as well as the catastrophic variety. Issues involving learning and convergence by fishers are considered as are complications arising from the hierarchical nature of fisheries. Policy responses to these problems are seen to involve the precautionary principle to mitigate the threat of catastrophic discontinuities and the scale-matching principle to ensure that management and property rights system are properly implemented.
TL;DR: In this article, a new mathematical model that describes segregation dynamics of two distinct populations in a city is presented, which associates segregation with an instability of a spatially uniform mixed population state.
Abstract: A new mathematical model that describes segregation dynamics of two distinct populations in a city is presented. The model associates segregation with an instability of a spatially uniform mixed population state. Segregated states correspond to alternating domains of overrepresentation and underrepresentation of a given population. A second instability designates a transition to a stronger form of segregation involving enclaves of pure population. The model is used to study neighborhood change processes such as displacements of transition zones and tipping point phenomena. The main significance of the model lies in the conceptual framework it introduces by relating sociospatial phenomena to dynamical system and pattern formation theories.
TL;DR: Simulation results are presented showing that the players' strategies acquired by evolutionary operator and the process to form parties in a negotiation are different according to the game rules.
Abstract: The dynamics of positions of political parties have been extensively studied by both numerical and agent-based approaches. We focus on the dynamics of formation and division of parties, particularly on how game rules to determine a winning party influences the agents' decision-making and process to reaching a consensus, and we perform an agent-based simulation using a game model called Spatial Voting Game. In this paper, we briefly describe the game as an environment of our agent-based simulation and learning architecture of agents for adaptive players in a multiagent system. Then we present simulation results showing that the players' strategies acquired by evolutionary operator and the process to form parties in a negotiation are different according to the game rules.
TL;DR: In this article, the relationship between social institutions and individual behaviour through the development of the cognitive framework of individuals is studied, and the problem of relativity of the cognition is studied through reconsideration of the conception of information and its transfer.
Abstract: This paper studies the relationship between social institutions and individual behaviour through the development of the cognitive framework of individuals. Social sciences have had interests in social institutions or norms. Much of the studies treat the problem from the viewpoint of social costs and lack focus on individual action and cognition. To consider the problem as a whole naturally means that the discussion has to be made according to subjectivism. Setting subjectivism forth as a premise, the problem of relativity of the cognition is studied through reconsideration of the conception of information and its transfer. By adopting a multi-agent model having the cognitive framework and the interaction among agents, the formation process and the feature of institutions are computationally investigated. Simulation results confirm that the cognitive frameworks of agents are affected action mimicking others' superficial behaviour. Moreover, it is eventually shown that the assumption of isolated individuals is unwarranted even in studying in less communicative communities.
TL;DR: A line of study by which Functional Magnetic Resonance Imaging can be used together with nonlinear dynamics concepts as a medium for the study of brain organization and the change in circuit patterns associated with aging is proposed.
Abstract: We propose a line of study by which Functional Magnetic Resonance Imaging (FMRI) can be used together with nonlinear dynamics concepts as a medium for the study of brain organization. The concentration is on (a) the complex behavior of elementary neural circuits, and how they interact over brief spans of time to produce cognition and memory; and (b) the change in circuit patterns associated with aging. The method of orbital decomposition appears to be ideally suited for these objectives and for determining how they integrate into hierarchical processes. The adapted procedure begins with a 3-D FMRI matrix of metabolic activity. Recurring patterns within a matrix row are identified and matched across rows and across depth slices. These hierarchical patterns are then compared over time for further recurrences. The computational procedure identifies the optimal pattern length over time, the patterns, and the largest Lyapunov for the system of patterns. Computations are assisted by statistical tests for the extent to which the isolated patterns represent the underlying data.
TL;DR: In this article, the second law of thermodynamics, Le Chatelie-Brown principle as universal laws are applied for nonlinear dynamical economic systems and the concept of parametric economic space is introduced, which reveals some conformities to natural universal laws allowing to advance the theory of evolutionary economics.
Abstract: The purpose of the present paper is to reveal some conformities to natural universal laws allowing to advance the theory of evolutionary economics. The second law of thermodynamics, Le Chatelie–Brown principle as universal laws are applied for nonlinear dynamical economic systems. The ergodic hypothesis is applied for dynamical economic systems as one from principles of economic forecasting. From the point of view of statistical physics, entropy is applied as universal function of a condition for economic systems. The evolution of economic dynamical systems at macro and microeconomic levels from the point of view of thermodynamics, statistical physics, and diffusion processes is investigated. The law of money circulation is formulated as one of the forms of display of energy conservation law in economic space. The concept of parametric economic space is introduced. The concepts of energy and number of degrees of freedom of a dynamical economic system allow substantiated cause and effect connections between the evolution of the system and a number of economic factors (forces), influencing on the system (degree of an openness, “freedom” of an economic system). The character of the development of technologies and the product life cycle are investigated as a nonlinear economic process. The concept of a wave function describing a technological wave connected with the entropy of a system of economic “cells” is introduced.
TL;DR: In this paper, the formation and stability of coalitions for a situation where finitely many individuals form different coalitions and their payoffs depend on the consequence of a non-cooperative game with different coalitional, and examine the moving path of individuals among various coalitions.
Abstract: We analyze the formation and stability of coalitions for a situation where finitely many individuals form different coalitions and their payoffs depend on the consequence of a noncooperative game with different coalitions, and examine the moving path of individuals among various coalitions. Our main finding is to show that there exists at least one evolutionarily stable coalition equilibrium in Γnx.