一个新型混沌系统的设计与电路实现

Design and Circuit Implementation of a New Chaotic System

为了研究混沌系统的性质及其应用,提出了一个新的三维混沌系统,该系统具有四个非线性项,包含三个二次交叉乘积项和一个完全平方项,此系统是具有新型的卷曲结构的混沌吸引子。对系统的耗散性、吸引子的存在性、平衡点的稳定性、Lyapunov指数及Lyapunov维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。最后进行了混沌系统的电路设计,电路实验结果和数值仿真一致,表明该混沌吸引子是物理存在的。

In order to study the properties and applications of chaotic systems,a new three-dimensional chaotic system with four nonlinear terms is proposed,including three quadratic cross product terms and a complete square term.The dissipation,existence of attractor,stability of equilibrium,Lyapunov index and dimension characteristics of the system are analyzed dynamically.The results show that the system has chaotic characteristics,complex dynamic behavior and sensitivity to system parameters.Finally,the circuit design of the chaotic system is carried out,and the experimental results are consistent with the numerical simulation,indicating that the chaotic attractor exists physically.