Transition to high-dimensional chaos in nonsmooth dynamical systems

TL;DR

This paper reveals a unique transition route from low- to high-dimensional chaos in nonsmooth dynamical systems, involving an intermediate nonchaotic regime, contrasting with the smooth systems' behavior.

Contribution

It identifies and analyzes a novel bifurcation route to high-dimensional chaos in nonsmooth systems, highlighting the role of periodic attractors as an intermediate state.

Findings

High-dimensional chaos emerges after a nonchaotic regime in nonsmooth systems.

The transition involves an abrupt appearance and disappearance of periodic attractors.

Numerical analysis supports the typicality of this transition route.

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. The finding has implications to applications where high-dimensional and robust chaos is desired.