In this article, a class of Chua’s system with smooth periodic nonlinear term is considered. This kind of systems exhibits strange dynamical behavior. Except for the existence of infinitely many equilibrium points, period-doubling bifurcation, and double-scroll attractors, this type of systems has strange dynamics different from the classical Chua’s system: (i) the coexistence of (infinitely) many non-chaotic strange attractors; (ii) the coexistence of (infinitely) many spiral chaotic attractors; (iii) the coexistence of multi-scroll attractors; (iv) “growing”-scroll attractors, where the number of scrolls is an increasing function with respect to the time variable.

本文考虑了一类具有平滑周期非线性项的蔡氏系统。这种系统表现出奇怪的动态行为。除了存在无限多的平衡点、倍周期分岔和双涡旋吸引子外，这类系统具有不同于经典蔡氏系统的奇异动力学：（i）（无限）许多非混沌奇异吸引子并存; （ii）（无限）许多螺旋混沌吸引子的共存；(iii) 多卷轴吸引子并存；(iv) “增长”-滚动吸引子，其中滚动的数量是关于时间变量的递增函数。