Routes to chaos in high-dimensional dynamical systems: A qualitative numerical study

Details Routes to chaos in high-dimensional dynamical systems: A qualitative numerical study Routes to chaos in high-dimensional dynamical systems: A qualitative numerical study

2004-08-06

arxiv.org/abs/nlin/0408017v1

Nonlinear Sciences

Chaotic Dynamics

17 pages, 8 figures

Scientific paper

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 $C^r$ mappings is outlined. The results comment on previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss.

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