Coexistence of Hidden Attractors in the Smooth Cubic Chua’s Circuit with Two Stable Equilibria

多稳态 吸引子 平衡点 混乱的 非线性系统 蔡氏电路 统计物理学 数学 拓扑(电路) 物理 数学分析 计算机科学 量子力学 组合数学 人工智能
作者
Irfan Ahmad,Banlue Srisuchinwong,Muhammad Usman Jamil
出处
期刊:International Journal of Bifurcation and Chaos [World Scientific]
卷期号:33 (04) 被引量:11
标识
DOI:10.1142/s0218127423300100
摘要

Since the invention of Chua’s circuit, numerous generalizations based on the substitution of the nonlinear function have been reported. One of the generalizations is obtained by substituting cubic nonlinearity for piece-wise linear (PWL) nonlinearity. Although hidden chaotic attractors with a PWL nonlinearity have been discovered in the classical Chua’s circuit, chaotic attractors with a smooth cubic nonlinearity have long been known as self-excited attractors. Through a systematically exhaustive computer search, this paper identifies coexisting hidden attractors in the smooth cubic Chua’s circuit. Either self-excited or coexisting hidden attractors are now possible in the smooth cubic Chua’s circuit with algebraically elegant values of both initial points and system parameters. The newly found coexisting attractors exhibit an inversion symmetry. Both initial points and system parameters are equally required to localize hidden attractors. Basins of attraction of individual equilibria are illustrated and clearly show critical areas of multistability where a tiny drift in an initial point potentially induces jumps among different basins of attraction and coexisting states. Such multistability poses potential threats to engineering applications. The dynamical regions of hidden and self-excited attractors, and areas of stability of equilibria, are illustrated against two parameter spaces. Both illustrations reveal that two nonzero equilibrium points of the smooth cubic Chua’s circuit have a transition from unstable to stable equilibrium points, leading to generations of self-excited and hidden attractors simultaneously.
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