English

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 5105 \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.

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