Magic Number 7 +- 2 in Globally Coupled Dynamical Systems?

Details Magic Number 7 +- 2 in Globally Coupled Dynamical Systems? Magic Number 7 +- 2 in Globally Coupled Dynamical Systems?

2002-04-10

arxiv.org/abs/nlin/0204013v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures, submitted to PRL

Scientific paper

The prevalence of Milnor attractors has recently been reported in a class of high-dimensional dynamical systems. We study how this prevalence depends on the number of degrees of freedom by using a globally coupled map and show that the basin fraction of Milnor attractors increases drastically around 5-10 degrees of freedom, saturating for higher numbers of degrees of freedom. It is argued that this dominance of Milnor attractors in the basin arises from a combinatorial explosion of the basin boundaries. In addition, the dominance is also found in a system without permutation symmetry, i,e., a coupled dynamical system of non-identical elements. Possible relevance to the magic number $7\pm 2$ in psychology is discussed.

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