Mathematik in den Naturwissenschaften Leipzig Routes to chaos in high-dimensional dynamical systems : a qualitative numerical study

This paper examines the most probable route to chaos a high-dimensional dynamical systems function space (time-delay neural networks) endowed with a probability measure in a computational setting. The most probable route to chaos (relative to the measure we impose on the function space) as the dimension is increased is observed to be a sequence of Neimark‐Sacker bifurcations into chaos. The analysis is composed of the study of an example dynamical system followed by a probabilistic study of the ensemble of dynamical systems from which the example was drawn. A scenario depicting the decoupling of the stable manifolds of the torus leading up to the onset of chaos in high-dimensional dissipative dynamical systems is also presented. c 2006 Elsevier B.V. All rights reserved.

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