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MiS Preprint

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

David Albers and J. Sprott


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.

MSC Codes:
05.45.-a, 89.75.-k
routes to chaos, bifurcation theory, high-dimensional dynamics

Related publications

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