193 research outputs found
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
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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
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