Dynamical formation of stable irregular transients in discontinuous map systems

TL;DR

This paper investigates the formation of stable irregular transients, known as stable chaos, in coupled discontinuous map systems, revealing a hidden phase space pattern and the role of boundary intersections in this phenomenon.

Contribution

It uncovers the mechanism behind stable chaos in discontinuous maps, showing how basin boundary interactions lead to long irregular transients.

Findings

Transient dynamics repeatedly approach and jump from basin boundaries.

Stable chaos originates from intersections of discontinuous boundaries and their images.

Numerical experiments verify the proposed mechanism.

Abstract

Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so far. In this paper, we investigate the dynamical formation of stable irregular transients in coupled discontinuous map systems. Interestingly, it is found that the transient dynamics has a hidden pattern in the phase space: it repeatedly approaches a basin boundary and then jumps from the bundary to a remote region in the phase space. This pattern can be clearly visualized by measuring the distance sequences between the trajectory and the basin boundary. The dynamical formation of stable chaos originates from the intersection points of the discontinuous boundaries and their images. We carry out numerical experiments to verify this mechanism.