Routes to chaos in high-dimensional dynamical systems: A qualitative numerical study
Chaotic Dynamics
2009-09-29 v1 Dynamical Systems
Abstract
This paper examines the most probable route to chaos in high-dimensional dynamical systems in a very general computational setting. The most probable route to chaos in high-dimensional, discrete-time maps is observed to be a sequence of Neimark-Sacker bifurcations into chaos. A means for determining and understanding the degree to which the Landau-Hopf route to turbulence is non-generic in the space of mappings is outlined. The results comment on previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss.
Keywords
Cite
@article{arxiv.nlin/0408017,
title = {Routes to chaos in high-dimensional dynamical systems: A qualitative numerical study},
author = {D. J. Albers and J. C. Sprott},
journal= {arXiv preprint arXiv:nlin/0408017},
year = {2009}
}
Comments
17 pages, 8 figures