Construction and Verification of a Simple Smooth Chaotic System

作     者：ZHANG Xiao-Dan SHI Feng WANG Zhen 

作者机构：School of Applied Science University of Science and Technology Beijing Beijing 100083 China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2007年第48卷第2X期

页      面：267-274页

核心收录：

学科分类：07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 070205[理学-凝聚态物理] 08[工学] 0704[理学-天文学] 0702[理学-物理学] 

基　　金：The project supported by National Natural Science Foundation of China under Grant Nos. 60074034 and 70271068 

主　　题：chaotic attractors three-dimensional quadratic autonomous dynamical system equilibrium point 

摘      要：This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equilibrium points respectively. Dynamical properties of this system are then studied. Furthermore, by applying the undetermined coefficient method, heteroclinic orbit of Shil＇nikov＇s type in this system is found and the convergence of the series expansions of this heteroclinic orbit are proved in this article. The Shil＇nikov＇s theorem guarantees that this system has Smale horseshoes and the horseshoe chaos.