The Shi’lnikov criterion shows that three-dimensional smooth autonomous differential equations can display chaos with the existence assumption of a heteroclinic cycle connecting saddle-focus equilibria. However, it is challenging to confirm this assumption in a given system, since common methods are to be developed. Although it has been partially extended to two-zone piecewise linear systems, there is very little work on piecewise systems with multiple discontinuous boundaries. This paper analytically investigates three types of heteroclinic cycles with a number of N in a new class of three-dimensional (N + 1)-zone non-smooth systems for arbitrary integer N ≥ 1. Moreover, the classical criterion above has been extended to the considered system with theoretical analysis as well as numerical experiments, where the developed criteria in this paper apply not only to systems exhibiting saddle-focus behavior but also to those possessing both saddle and saddle-focus equilibria. In addition, the existence conditions established for chaos induced by N heteroclinic cycles in this work, generalize the previous reported case of N = 1, 2 to the case of arbitrary N ≥ 1.

杨启贵教授，博士(后)，华南理工大学二级教授，博士生导师，校教学名师。主要从事混沌机理、动力系统几何理论、混沌系统与随机系统复杂性、非线性电路及其应用、经济混沌动力系统等研究。讨论系统简单到何种程度仍然具有混沌复杂性，揭示混沌系统混沌机理与复杂动力学特征。在混沌动力系统复杂性及混沌机理、混沌与超混沌系统的构造、分岔与随机动力系统复杂性、矩阵微分系统振动理论及其相关应用中取得了一定成效。主持国家自然科学基金6项、省部级基金7项，省部级教研项目13项等。已培养出站博士后合作研究人员5人，毕业博士研究生25人、硕士研究生38人，在读博士5人、硕士5人，其中3人博士学位论文获广东省优秀博士学位论文等。