摘要
提出了一个新的三维混沌系统。通过调节系统中的参数,使系统在保持混沌动力学行为的同时分别具有多种类型的平衡点,即一个不稳定平衡点、无平衡点、无穷平衡点和一个稳定平衡点。此外,随着参数和初始值的变化,发现系统是一个大范围的混沌系统,且在无对称性条件下具有共存吸引子。分析了系统的基本动力学行为,包括系统的相图、Lyapunov指数谱和分岔图。利用拓扑马蹄理论和数值计算,找到了系统的拓扑马蹄,并获得拓扑熵,进一步从理论上证明系统的混沌特性。
A new three-dimensional chaotic system was proposed.By adjusting system parameters,the system may have multiple types of equilibrium points,such as an unstable equilibrium point,no equilibrium point,infinite equilibrium points and a stable equilibrium point,while maintaining its chaotic dynamical behaviors.In addition,with the change of parameters and initial values,it is found that the system is a large-scale chaotic system and has coexistence attractors under the condition of asymmetry.The system’s basic dynamic behaviors were analyzed by using the phase diagram,Lyapunov exponent spectrum and bifurcation diagram.By virtue of topological horseshoe theory and by means of numerical calculations,the system’s topological horseshoe and topological entropy were obtained,which further proves its chaotic characteristics in theory.
作者
徐昌彪
钟德
郭桃桃
XU Changbiao;ZHONG De;GUO Taotao(School of Optoelectronic Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;School of Communication and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2020年第9期235-241,247,共8页
Journal of Vibration and Shock
基金
国家自然科学基金青年科学基金(61602073)。
关键词
混沌系统
平衡点
大范围
拓扑马蹄
chaotic system
equilibrium point
large range
topological horseshoe
