具有复合幂函数的混沌系统的设计与仿真  

Design and Circuit Simulation of Chaotic System with a Composite Power Function

作　　者：徐启程[1] 孙常春[1] 邢祥宇 XU Qi-cheng;SUN Chang-chun;XING Xiang-yu(School of Science,Shenyang Jianzhu University,Shenyang 110168,China;School of Information and Control Engineering,Shenyang Jianzhu University,Shenyang 110168,China)

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168 [2]沈阳建筑大学信息与控制工程学院,辽宁沈阳110168

出　　处：《控制工程》2021年第11期2261-2265,共5页Control Engineering of China

基　　金：辽宁省教育厅自然科学基金资助项目(lnqn201919)。

摘　　要：构造了一类新的三维连续自治混沌系统,该系统含有三个非线性项,其中一项是指数小于1的复合幂函数,给出了系统的混沌吸引子相图,对系统的耗散性、吸引子的存在性、平衡点的稳定性、Lyapunov指数特性进行了动力学分析。结果表明此系统具有混沌特性,具有复杂的动力学行为且对系统参数具有敏感性,进行了混沌系统的电路设计,从而进一步说明了提出的系统具有丰富的动力学特性以及有效性。A new three-dimensional continuous autonomous chaotic system with three nonlinear terms is constructed. A nonlinear term is a composite power function with an exponent less than 1. Phase diagrams of a chaotic attractor for the system are given. Dynamical behaviors including the dissipation of the system, the existence of the attractor, the stability of each equilibrium point and the characteristics of Lyapunov exponent are analyzed. The results show that the system has chaotic characteristics, complex dynamical behaviors and the sensitivity to system parameters. The circuit design of the chaotic system is carried out. The simulation result illustrates that the proposed system has rich dynamic characteristics and the effectiveness.

关 键 词：混沌系统 动力学分析 LYAPUNOV指数 电路仿真 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]