一类三维货币混沌系统的动力学分析  

Study on nonlinear dynamics of a financial chaotic system

作　　者：张勇[1] 杨雪玲[2] 舒永录[3] ZHANG Yong;YANG Xue-ling;SHU Yong-lu(Department of Basic Teaching, Henan Polytechnic Institute, Nanyang 473000, China;Department of Automobile Engineering, 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]河南工业职业技术学院汽车工程学院,河南南阳473000 [3]重庆大学数学与统计学院,重庆401331

出　　处：《东北师大学报（自然科学版）》2018年第2期165-168,共4页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11171360)

摘　　要：根据动力系统的理论与方法,研究了一类三维连续金融动力系统的一些重要非线性动力学特性,如平衡点及其拓扑类型、正向不变集、吸引域、吸引子的性质等,给出了这类三维连续金融系统全局吸引集的解析表达式,并且用计算机软件进行了相应的计算机仿真.结果表明,这些混沌动力学特性有助于加深人们对各种金融政策的理解,该混沌系统可应用于控制工程、图像加密等领域中.Based on the theory and the method of dynamical systems,this paper investigates some important dynamics of a financial chaotic system,such as the equilibria and its stability,positively invariant sets,global exponential attractive sets,chaotic attractors,and this paper gets a family of mathematical expressions of global exponential attractive sets for this financial chaotic system with respect to the parameters of this financial chaotic system.An extensive numerical simulation is performed to validate the analytic findings.The chaotic dynamics help deepen people’s understanding of various financial policies.This financial chaotic system is expected to be applied in the control engineering,image encryption,and other fields.

关 键 词：动力系统 稳定性理论 平衡点 不变集 计算机仿真 

分 类 号：O241.84[理学—计算数学] O29[理学—数学]