Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2004-08-20
Nonlinear Sciences
Adaptation and Self-Organizing Systems
22 pages, 23 figures; updated references, corrected typos, changed content
Scientific paper
10.1016/j.physd.2005.06.031
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.
Akiyama Eizo
Crutchfield James P.
Sato Yuzuru
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