基于线性反馈控制的超混沌系统设计与电路实现

Design and circuit implementation of hyperchaotic system based on linear feedback control

基于最新提出的简化Lorenz混沌系统,采用线性控制策略,设计了一个超混沌系统。利用相图、Lyapunov指数谱、分岔图以及Poincaré截面分析方法,详细地研究了系统参数变化时简化Lorenz超混沌系统的动力学行为,数值仿真结果显示,Lyapunov指数谱与分岔图分析一致。采用分立元件,设计并实现了该系统的模拟电子电路,通过调节电路中的可变电阻,观察到了该系统的极限环、叉式分岔、倍周期分岔、混沌和超混沌,以及由倍周期分岔而进入混沌的道路等动力学现象。数值仿真和电路实验结果表明,该系统具有丰富的动力学特性,且电路实验结果与数值仿真相吻合。

A hyperchaotic system is investigated by applying a linear feedback controller to the simplified Lorenz chaotic system.Dynamics of the simplified Lorenz hyperchaotic system is analyzed in details by using the phase diagrams,Lyapunov exponent spectrum,bifurcation diagrams,and the Poincaré sections with the system parameter variation.Numerical simulation results indicate that Lyapunov exponent spectrums are consistent with bifurcation diagrams.An analog circuit of the hyperchaotic system is designed and implemented with discrete components.By regulating the variable resistor in the circuit,dynamic behaviors,including limit cycle,pitchfork bifurcation,period-doubling bifurcation,chaos,hyperchaos and the route to chaos by period-doubling bifurcation,are observed.The results show that the system has complex dynamic properties,and circuit experiment results and numerical simulation are identical with each other.