Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems

Abstract

Dominance of Milnor attractors in high-dimensional dynamical systems is reviewed, with the use of globally coupled maps. From numerical simulations, the threshold number of degrees of freedom for such prevalence of Milnor attractors is suggested to be $5\sim 10$, which is also estimated from an argument of combinatorial explosion of basin boundaries. Chaotic itinerancy is revisited from the viewpoint of Milnor attractors. Relevance to neural networks is discussed.

16 pages including 3 figures, for the proceedings of NATO ASI on Synchronization