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

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 cri...

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Veröffentlicht in:Chaos (Woodbury, N.Y.) N.Y.), 2022-08, Vol.32 (8), p.081106-081106
Hauptverfasser: Leo Kingston, S., Kapitaniak, Tomasz, Dana, Syamal K.
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Sprache:eng
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Zusammenfassung: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.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0108401