一个新混沌系统及其拓扑马蹄分析  

New Chaotic System and Analysis of Its Topological Horseshoe

作　　者：王春梅[1] 胡春华[2] 薛华[3] WANG Chunmei HU Chunhua XUE Hua(Department of Information Engineering Department of Electrical Engineering College of Aeronautical Engineering, Binzhou University, Binzhou 256600, China)

机构地区：[1]滨州学院信息工程系,山东滨州256600 [2]滨州学院电气工程系,山东滨州256600 [3]滨州学院航空工程系,山东滨州256600

出　　处：《济南大学学报（自然科学版）》2017年第4期318-322,共5页Journal of University of Jinan(Science and Technology)

基　　金：山东省自然科学基金项目(ZR2014FQ019);滨州学院科研基金项目(BZXYG1302;BZXYG1618)

摘　　要：为了进一步丰富混沌系统理论及类型,提出一个新的三维混沌系统,分析该系统的基本动力学特征,研究该系统混沌吸引子的形成机理,通过系统相图、Lyapunov指数谱图和分岔图等数学仿真方法验证系统的混沌特性,借助Poincaré映射和拓扑马蹄映射理论,找到系统的拓扑马蹄,进一步从理论上证明系统的混沌特性。结果表明,该系统的混沌吸引子是通过2个简单吸引子的镜像映射融合而成的复合结构,并且该系统与广义Lorenz系统不拓扑等价,是一种新混沌系统。To enrich the theory and types of chaotic systems, a new three-dimensional chaotic system was presented. Basic dynamic properties and the forming mechanism of chaotic attractor of the system were analyzed. Chaotic behaviors of the system were illustrated by using numerical simulations including phase portraits, Lyapunov exponents, and bifurcation diagram. The existence of topological horseshoe in the new system was proved via Poincare map and topological horseshoe map theory. The results show that the chaotic attractor has a compound structure merging together by a mirror operation of two simple attractors. The system is not equivalent to the generalized Lorenz system and it is a novel chaotic system.

关 键 词：混沌系统 单涡卷控制 POINCARÉ映射 拓扑马蹄 

分 类 号：TP914[自动化与计算机技术]