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arXiv · 2209.05196

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

S. Leo Kingston·Tomasz Kapitaniak·Syamal K. Dana
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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.

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S. Leo Kingston, Tomasz Kapitaniak, Syamal K. Dana. 2022-08-31. Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems. https://doi.org/10.1063/5.0108401

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