Adaptive Dynamics for Interacting Markovian Processes

Dynamics of information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for Markovian processes and study its behavior to observe information flow through the system. Examples of the adaptive dynamics for two stochastic processes interacting through matching pennies game interaction are exhibited along with underlying causal structure

Stability and Diversity in Collective Adaptation

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by information flux between agents, giving a novel view of collective adaptation.Comment: 22 pages, 23 figures; updated references, corrected typos, changed conten

Random dynamics from a time series of physiological rhythms

A random dynamics with two stochastic terms is modeled based on a time series of physiological experimental data to study synchrony between human heartbeats and pedaling rhythms modulated by music. We observe reproduced time series, rotation numbers, and invariant densities in the model to explain transitory stagnation motion of synchrony in the experiments.\u

Random Dynamics from Time Series of Rotating Fluid

A random dynamics is extracted from time series of laminar-turbulent transition in rotating fluid\ud in an open cylinder. We focus on the dynamics of the surface height in the central region and\ud measure switching dynamics between different quasi-stationary states and intensity of underlying\ud turbulence. Density of return map is constructed from an one dimensional map with an stochastic\ud term from the experimental data. It is shown that the random dynamics whose noise amplitude\ud depends on the slow variable describes the observed macroscopic features of rotating fluid in terms\ud of noise-induced phenomena