Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland.
Chaos. 2022 Aug;32(8):081106. doi: 10.1063/5.0108401.
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.
超混沌通过存在至少两个正的李雅普诺夫指数与混沌相区别，而不仅仅是在动力系统中存在一个。本文提出了一个一般情况，表明当时间动力学表现出间歇性的大振幅尖峰或爆发事件时，连续动力系统的吸引子突然在临界参数处发生超混沌，会出现超混沌。时间动力学的局部最大值分布是非高斯的，有一个尾部，这证实了大振幅事件的罕见发生。我们在三个典型模型中，即耦合 Hindmarsh-Rose 模型、三个耦合的 Duffing 振荡器和一个超混沌模型中，例证了我们的结果。
