Chaotic saddles and interior crises in a dissipative nontwist system

TL;DR

This paper investigates how chaotic saddles form and cause interior crises in a dissipative nontwist system, revealing their role in sudden attractor expansion and complex transient dynamics.

Contribution

It introduces the creation of chaotic saddles in a dissipative nontwist map and analyzes their role in interior crises and crisis-induced intermittency.

Findings

Chaotic saddles are responsible for interior crises in the system.

Presence of two saddles increases transient times.

Crisis induces intermittency in the system's dynamics.

Abstract

We consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems, they are responsible for chaotic transients, fractal basin boundaries, chaotic scattering and they mediate interior crises. In this work we discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. We show how the presence of two saddles increase the transient times and analyze the phenomenon of crisis induced intermittency.