English

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 CrC^r 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

R2 v1 2026-07-22T18:12:38.681Z