Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2002-02-17
Nonlinear Sciences
Adaptation and Self-Organizing Systems
29 pages, 10 figures
Scientific paper
10.1016/S0167-2789(03)00100-3
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given as a dynamical system of a 1-dimensional map. Through the time evolution of this system, a dynamical graph (a network) emerges. This graph has three interesting properties: i) vertices appear as stable elements, ii) the terminals of directed edges change in time, and iii) some vertices determine the dynamics of edges, and edges determine the stability of the vertices, complementarily. Two aspects of FD are studied, the generation of a graph (network) structure and the dynamics of this graph (network) in the system.
Kaneko Kunihiko
Kataoka Naoto
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