一个新混沌系统及其拓扑马蹄分析
发布时间：2019-02-18 19:33
【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。
[Abstract]:In order to further enrich the theory and types of chaotic system, a new three-dimensional chaotic system is proposed. The basic dynamic characteristics of the system are analyzed, and the formation mechanism of chaotic attractor is studied. The chaotic properties of the system are verified by mathematical simulation methods such as Lyapunov exponent spectrum diagram and bifurcation diagram. The topological horseshoe of the system is found by using Poincar 茅 mapping and topological horseshoe mapping theory, and the chaotic property of the system is further proved theoretically. The results show that the chaotic attractor of the system is a composite structure formed by the fusion of two simple attractors' mirrored maps, and the system is not topological equivalent to the generalized Lorenz system, so it is a new chaotic system.
【作者单位】： 滨州学院信息工程系;滨州学院电气工程系;滨州学院航空工程系;
【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)
【分类号】：O415.5
，
本文编号：2426134
[Abstract]:In order to further enrich the theory and types of chaotic system, a new three-dimensional chaotic system is proposed. The basic dynamic characteristics of the system are analyzed, and the formation mechanism of chaotic attractor is studied. The chaotic properties of the system are verified by mathematical simulation methods such as Lyapunov exponent spectrum diagram and bifurcation diagram. The topological horseshoe of the system is found by using Poincar 茅 mapping and topological horseshoe mapping theory, and the chaotic property of the system is further proved theoretically. The results show that the chaotic attractor of the system is a composite structure formed by the fusion of two simple attractors' mirrored maps, and the system is not topological equivalent to the generalized Lorenz system, so it is a new chaotic system.
【作者单位】： 滨州学院信息工程系;滨州学院电气工程系;滨州学院航空工程系;
【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)
【分类号】：O415.5
，
本文编号：2426134
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