不对称非线性蔡氏电路产生的混沌现象分析

Analysis of chaos in asymmetric nonlinear Chua's circuit

为了更确切地描述实际系统中的混沌现象,提出了一种变形蔡氏电路,它含有一个不对称非线性阻性元件。对该电路进行了深入的数学分析;并在MATLAB环境下,对其产生的混沌现象进行了仿真分析。分析结果表明:改变电路中的线性电阻值R,可以观察到直流平衡态、Hopf分岔、倍周期分岔、单涡卷混沌吸引子、周期性窗口和不对称双涡卷混沌吸引子等非线性动力学行为;混沌系统对初始条件极其敏感;不对称非线性蔡氏电路有其特殊的性质。

In order to describe the actual chaotic systems exactly, a simple modified Chua＇s circuit is presented, which includes an asymmetric nonlinear resistive element. Mathematical analysis is performed first, and then the simulation study is completed in MATLAB. By changing the value of linear resistor R in the circuit, dynamical behaviors are observed, such as DC equilibrium point, Hopf bifurcation, period-doubling bifurcation, single-scroll strange attractor, periodic window and asymmetric double-scroll strange attractor. The extreme sensitivity in the state trajectory with respect to the initial conditions is exhibited, and the special characteristic of the asymmetric nonlinear Chua＇s circuit is observed also.