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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
92/2005

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

David Albers and J. Sprott

Abstract

This paper examines the most probable route to chaos in high-dimensional dynamical systems in a general computational setting (time-delay neural networks). The most probable route to chaos in high-dimensional, discrete-time maps (relative to our construction) 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. Finally, a scenario regarding the onset of chaos in high-dimensional dissipative dynamical systems where the strongly stable directions with rotation decouple before chaos onsets is presented.

Received:
Oct 24, 2005
Published:
Oct 24, 2005
MSC Codes:
37XX
PACS:
05.45.-a, 89.75.-k
Keywords:
routes to chaos, bifurcation theory, high-dimensional dynamics

Related publications

inJournal
2006 Repository Open Access
David J. Albers and J. C. Sprott

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

In: Physica / D, 223 (2006) 2, pp. 194-207