Chaotic Switching In The Minimal Pendula Network

TL;DR

This paper investigates chaotic switching phenomena in a minimal network of three globally coupled pendula, identifying bifurcation scenarios and analyzing stability to understand complex dynamical behaviors.

Contribution

It introduces new insights into chaotic switching mechanisms in minimal pendula networks, detailing bifurcation scenarios and stability conditions for chimera states.

Findings

Identified three scenarios of chaotic switching: riddling bifurcation, blowout bifurcation, and saddle chimera switching.

Analyzed stability conditions of chimera states and their dependence on system parameters.

Observed that chaotic chimeras can escape to stable solutions, adding unpredictability.

Abstract

We report the chaotic switching phenomenon in the minimal $N = 3$ pendula network with global coupling. Analyzing the stability conditions of the chimera states and their dependence on the parameters, three scenarios of chaotic switchings are identified: 1) a riddling bifurcation scenario, where an unstable periodic orbit inside the chimera manifold becomes transversally unstable, 2) a blowout bifurcation scenario, where the switching is caused by the transverse destabilization of the chaotic chimera with respect to its manifold, and 3) switchings between "laminar" saddle chimeras within a global "turbulent" attractor. The results are obtained based on the detailed examination of the existing regimes including chimera states, limit cycles and fixed points, their multistability and switching regime. In the parameter regions where the chaotic chimeras coexist with stable non-chaotic solutions, the switching trajectory can eventually escape to a stable solution, causing an additional unpredictability in the system behavior, as it is difficult to predict the escaping moment.