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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.