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 ~ 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.