Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems

TL;DR

This paper presents a general scenario for the sudden transition to hyperchaos in dynamical systems, characterized by a rapid attractor expansion and intermittent large-amplitude events, confirmed through three different models.

Contribution

It introduces a universal scenario for hyperchaos emergence involving attractor expansion and intermittent events, validated across multiple dynamical system models.

Findings

Hyperchaos emerges suddenly at a critical parameter value.

Large-amplitude events follow a non-Gaussian distribution with a tail.

The scenario is demonstrated in three different models.

Abstract

Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large expansion of the attractor of continuous dynamical systems at a critical parameter when the temporal dynamics shows intermittent large-amplitude spiking or bursting events. The distribution of local maxima of the temporal dynamics is non-Gaussian with a tail, confirming a rare occurrence of the large-amplitude events. We exemplify our results on the sudden emergence of hyperchaos in three paradigmatic models, namely, a coupled Hindmarsh-Rose model, three coupled Duffing oscillators, and a hyperchaotic model.