Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems
Chaotic Dynamics
2007-05-23 v1
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 , 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.
Keywords
Cite
@article{arxiv.nlin/0302038,
title = {Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems},
author = {Kunihiko Kaneko},
journal= {arXiv preprint arXiv:nlin/0302038},
year = {2007}
}
Comments
16 pages including 3 figures, for the proceedings of NATO ASI on Synchronization