含一个绝对值项的新三维混沌系统  

A New Three-Dimension Chaotic System with an Absolute Item

作　　者：刘金梅[1] 丘水生[2] 

机构地区：[1]暨南大学信息科学技术学院,广东广州510632 [2]华南理工大学电子与信息学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2013年第4期137-141,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(21310018;61077030);广东省科技计划国际合作项目(2010B050900016);广东省自然科学基金资助项目(9151170003000013)

摘　　要：通过增加绝对值项,构造了一种新的三维混沌系统,对其动力学特性进行了研究.借助于混沌理论和数值仿真,分析了系统的平衡点性质、Lyapunov维数、Poincaré截面、最大Lyapunov指数谱、分岔图等.结果表明:所提出的三维自治系统具有分数维、多个不稳定的平衡点以及层次结构的Poincaré映射,在较广的参数范围内呈现出混沌特性;系统可以产生四翼混沌吸引子,具有复杂的动力学特性.In this paper, a new three-dimension chaotic system is constructed by adding an absolute item in the system, and the dynamic properties of the new system are investigated. Then, by virtue of the chaos theory and the numerical simulation, the equilibrium point, the Lyapunov dimension, the Poincar6 section, the largest Lyapunov exponent spectrum and the bifurcation diagram of the system are analyzed. It is indicated that the proposed threedimension autonomous system exhibits chaotic features in a wide parameter range and is of fractional dimension, multiple unstable equilibrium points and layered Poincar6 mapping. Moreover, Owing to its complex dynamic properties ,the system can generate four-wing chaotic attractors.

关 键 词：混沌 吸引子 LYAPUNOV指数 POINCARÉ截面 分岔图 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]