This paper examines the most probable
route to chaos [in] 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.
Ref: D. J. Albers and
J. C. Sprott, Physica
D
223,
194-207 (2006)