一类分段线性连续动力系统的边界混沌分岔  

Boundary Chaos Bifurcation in a Class of Piecewise-linear Continuous Dynamical Systems

作　　者：王磊 张晓倩 WANG Lei;ZHANG Xiao-qian(School of Artificial Intelligence and Big Data,Hefei University,Hefei 230601,China)

机构地区：[1]合肥大学人工智能与大数据学院,中国合肥230601

出　　处：《湖南师范大学自然科学学报》2024年第4期121-127,共7页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(12302034);安徽省高等学校自然科学基金重点项目(KJ2021A0996);合肥大学数学重点学科项目(2023xk06)。

摘　　要：研究了一类三维分段线性连续系统从稳定平衡点突变到混沌不变集的边界平衡点分岔现象。首先,验证了同宿轨和异宿轨的不存在性,从而说明系统的混沌现象是非Shil'nikov混沌。进一步,通过在切换面上寻找合适的Poincaré截面,并通过两个子系统混合流作用建立二次返回Poincaré截面映射,再利用拓扑马蹄理论,给出系统混沌不变集存在性的计算机辅助证明。We investigate a striking boundary equilibrium bifurcation from a stable equilibrium to a chaotic invariant set for a class of three-dimensional piecewise-linear continuous systems.Firstly,the nonexistence of homoclinic and heteroclinic orbits is verified,which shows that the chaos phenomenon of the systems is non-Shil nikov chaos.Further,by finding the appropriate Poincarécross section on the switching plane,we build the second return Poincarémap through the mixed flow of two subsystems.Moreover,a computer assisted verification of chaotic invariant sets is presented by the topological horseshoe theory.

关 键 词：分岔 渐近稳定 混沌 拓扑马蹄 分段线性系统 

分 类 号：O193[理学—数学]