Abstract

We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors in between the regimes of low- and high-dimensional chaos. That is, the emergence of high-dimensional chaos is preceded by the system's settling into a totally nonchaotic regime. This is characteristically distinct from the situation in smooth dynamical systems where high-dimensional chaos emerges directly and smoothly from low-dimensional chaos. We carry out an analysis to elucidate the underlying mechanism for the abrupt emergence and disappearance of the periodic attractors and provide strong numerical support for the typicality of the transition route in the pertinent two-dimensional parameter space. In view of the previous understanding that chaos is typically robust (i.e., without periodic windows) in nonsmooth dynamical systems, the occurrence of a parameter regime of periodic attractors between low- and high-dimensional chaos is unexpected. The finding has implications to applications where high-dimensional and robust chaos is desired.

Original languageEnglish (US)
Article number052212
JournalPhysical Review E
Volume98
Issue number5
DOIs
StatePublished - Nov 13 2018

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dynamical systems
chaos
Chaos
High-dimensional
Dynamical system
Attractor
routes
settling
Parameter Space
Bifurcation
occurrences
intervals
Distinct
Interval

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Transition to high-dimensional chaos in nonsmooth dynamical systems. / Du, Ru Hai; Qu, Shi Xian; Lai, Ying-Cheng.

In: Physical Review E, Vol. 98, No. 5, 052212, 13.11.2018.

Research output: Contribution to journalArticle

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