异结构超混沌系统的自适应函数投影同步

Adaptive Function Projective Synchronization of Different Hyper Chaotic Systems

针对异结构分数阶和整数阶超混沌系统的函数投影同步(FPS)及其响应系统参数识别问题,利用Laplace变换将分数阶微分变换到Laplace域中,然后再利用整数阶微分来逼近分数阶微分,把异结构(分数阶和整数阶)混沌系统的同步问题转化为同结构(整数阶)系统的同步。利用缩减驱动系统维数以达到驱动、响应系统维数一致。根据Lyapunov稳定性理论,设计了非线性控制输入机制和参数更新规则。MATLAB数值仿真结果验证了所设计的控制器和参数更新规则的有效性。所提的内容为整数阶和分数阶的有关同步提供了一种新的思考方法。

For the problem of the function projective synchronization between fractional-order and integer-order hyperchaotic systems and parameter identification of the response system, the Laplace transform is used to transform the fractional-order differential into the Laplace domain. By using the integral order differential to approximate the fractional order operators, the problem of synchronization of different chaotic systems(fractional order and integer order) is transformed into the problem of the synchronization of same structure integer-order chaotic systems. The dimension of drive system is reduced to achieve the same dimensions of drive and response systems. According to the Lyapunov stability theory, the nonlinear control input mechanism and parameter updating rules are designed. The validity of the designed controller and parameter updating rules is verified through numerical simulation of MATLAB.This paper provides a new train of thought for the synchronization of integer order and fractional order chaotic systems.