具有复合幂函数和共存吸引子的新混沌系统的动力学分析与电路仿真  

Dynamics Analysis and Circuit Simulation of A New Chaotic System with A Compound Power Function and Coexisting Attractors

作　　者：徐启程[1] 孙常春[1] XU Qicheng;SUN Changchun(School of Science,Shenyang Jianzhu University,Shenyang,Liaoning 110168,China)

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168

出　　处：《计算物理》2021年第6期742-748,共7页Chinese Journal of Computational Physics

基　　金：辽宁省教育厅科学研究基金(lnqn201919)资助项目。

摘　　要：构造一个具有复合幂函数的三维连续自治混沌系统。系统的状态方程仅有5项,其中一项是指数小于1的复合幂函数。该系统具有结构简单、非双曲平衡点、吸引子共存的性质,展现出了复杂的动力学行为。首先,对系统的动力学行为进行分析,包括李雅普诺夫(Lyapunov)指数谱、分岔图以及庞加莱映射等,结果表明此系统具有混沌特性。然后进行混沌系统的电路设计,电路仿真结果验证了理论分析的正确性。A new three-dimensional continuous autonomous chaotic system with a compound power function is constructed.The equation of state of the system has only five terms,one of which is a compound power function with an exponent less than 1.The system has properties of simple structure,non-hyperbolic equilibrium point,coexistence of attractors,and exhibits complex dynamic behaviors.Firstly,dynamic behaviors including Lyapunov exponential spectrum,bifurcation diagram and Poincarémapping are analyzed.It shows that the system has chaotic characteristics.Then,circuit design of the chaotic system is carried out.Circuit simulation results verify the theoretical analysis.

关 键 词：混沌系统 复合幂函数 共存吸引子 动力学分析 电路仿真 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]