Dynamical analysis of a class of generalized Chua’s systems with infinitely many attractors

Abstract

The study of the existence of finitely many chaotic attractors in the Chua’s system is a classical topic. In this article, a class of generalized Chua’s systems is introduced, where the nonlinear items are extended by a type of polynomial functions. The existence of infinitely many chaotic attractors is studied, which can not be observed in the classical Chua’s system. A lot of interesting dynamical behavior can be obtained in this kind of systems under certain conditions: (i) the coexistence of infinitely many self-excited attractors; (ii) the existence of multi-scroll attractors as well as strange dynamics with growing-scroll, where growing-scroll refers to the number of the scrolls of the attractors is increasing as time is increasing; (iii) the coexistence of infinitely many hidden attractors. Furthermore, the circuit simulations for two examples from this kind of generalized Chua’s systems illustrate the possible existence of infinitely many hidden and multi-scroll attractors under certain conditions.