新三维自治混沌系统动力学性质研究  

Analysis Dynamics Character of a Novel 3D Chaotic System

作　　者：张勇[1] 胡永才[1] 舒永录[2] ZHANG Yong HU Yong-cai SHU Yong-lu(Department of Basic Teaching, Henan Polytechnic Institute, Nanyang 473000, China College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)

机构地区：[1]河南工业职业技术学院基础教学部,河南南阳473000 [2]重庆大学数学与统计学院,重庆401331

出　　处：《数学的实践与认识》2017年第19期217-223,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目(11171360)

摘　　要：采用动力系统理论分析和计算机数值仿真相结合的方法,研究了一类新三维自治混沌系统的非线性动力学行为,如平衡点及其稳定性、不变集、混沌吸引子、吸引域等,从而展示了该混沌系统的丰富的动力学特性并且用matlab给出了相应的计算机模拟.创新点在于同时考虑了该混沌系统的最终界和全局吸引集,并且对于这个混沌系统的任意正参数,分别得到了该混沌系统最终界的一个参数族数学表达式和全局指数吸引集的一个参数族数学表达式,最后利用交集的思想分别得到了混沌系统最终界和全局吸引集的一个较小的数学表达式.混沌系统有望在实际保密通信中得到应用.Some dynamics of a new chaotic system are studied in this paper by theoretical analysis of the dynamical systems and computer simulation. The equilibrium point and its stability, invariant set, attractor, domain of attraction of this chaotic system are studied. It shows that this chaotic system has rich dynamic characteristics. The innovation point of this paper is that the ultimate bound and the global attractive sets are both considered in this paper and a family of mathematical expressions of the ultimate bound and the global attractive sets for the system are both obtained. And we can a smaller bound of the ultimate bound and the global attractive sets for this system by the intersection of all the sets. This chaotic system is expected to be applied in secure communication.

关 键 词：混沌系统 混沌吸引子 李雅普诺夫稳定性 平衡点 

分 类 号：O415.5[理学—理论物理]