MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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.

Oct 24, 2005
Oct 24, 2005
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