具有恒Lyapunov指数谱的新三维混沌系统分析与电路实现

A novel three- dimensional chaotic system analysis with invariable Lyapunov exponent spectrum and its circuit implementation

构造一个新三维自治混沌系统,它是Lorenz系统、Chen系统和Lü系统的通式.通过其Lyapunov维数、Lyapunov指数谱、分岔图分析了当系统不同参数变化时的动力学特性.其Lyapunov指数谱说明该系统存在双恒Lyapunov指数混沌锁定;分岔图和状态变量幅值演变说明锁定后混沌系统的幅值与相位可以调节.最后,设计了该混沌系统的电路实现并用Multisim软件对该电路进行仿真,结果验证了理论分析与电路仿真具有一致性.

A novel three- dimensional autonomous chaotic system is constructed,which is the general structure of the Lorenz system,Chen system and Lü system. The dynamic properties of the new system are analyzed via Lyapunov dimension,Lyapunov exponent spectrum,bifurcation diagrams when system parameters vary. The Lyapunov exponent spectrum is locked when the parameters of the quadratic cross- product terms vary. The bifurcation diagrams and state variable evolutions of the locked chaotic systems show that the amplitude evolvement and the phase of the chaos signals can be modulated. Finally,the circuit of the new chaotic system is designed and realized by Multisim software,and results show a good agreement between theory analysis and circuit simulations.