Lorenz系统的混沌同步与保密通信

提出一种用于2个Lorenz系统混沌同步的非线性反馈方法。用Lyapunov第二定理证明2个Lorenz系统的误差系统零点稳定性和2个Lorenz系统的同步,在Matlab上进行了数值仿真。结果表明:响应系统与驱动系统同步的条件是它们的参数必须相同,而与响应系统的初值无关。提出了一种保密通信的方案,信息信号m(t)调制到混沌变量x(t)成为混沌传输信号s(x,m),响应系统与驱动系统同步的条件是它们有共同的方程结构和参数。所以驱动系统的方程结构和参数(σ,ρ,β)作为可解调密钥,控制2个系统的同步,从而将信息复原,实现混沌保密通信。

Chaotic synchronization of Lorenz systems and secure communication

The chaotic synchronization of Lorenz systems are investigated via a nonlinear feedback method.The stability in zero of the error dynamical system of the two Lorenz systems is verified by the second Lyapunov method.The synchronization conditions are that two systems have the same equation construction and the same parameters and no relation to the initial values of the response system.A schem of chaotic communication based on the chaotic synchronization is presented.The message signals is mixed to the chaotic drive signals to be the pretend transmitted signals.The equation construction and the parameters of the response system can be the cipher based on the synchronization to control the synchronization of two systems.The message signals are recovered and the secure communication is achieved.