基于线性耦合下混沌系统的同步条件

The synchronization condition of linearly coupled chaotic system

将混沌同步问题用精确的数学语言给予描述,通过数学分析将其转化为微分方程组的稳定性问题.以Lorenz系统族的Chen氏系统作为典型系统,在线性耦合下分析系统参数,得到了系统达到同步时的充分条件,且在理论上加以证明.结合该条件,提出了一种确定耦合系数的方法.最后用仿真实验验证了该方法的正确性,并验证了在不同耦合方式和参考系统的情况下定理的有效性.

We describe the problem of chaos synchronization with rigorous mathematical theory, and convert it to the analysis of stability of the differential equations. Chen＇s system, which belongs to the Lorenz＇s group, has been introduced as a typical system for discussing the stability of the linear coupled chaotic systems. A theorem on the sufficient conditions for attaining the chaotic synchronization has been proposed and a detailed proot is given. Using the conditions discussed above, a method of identifying the coupled parameter is also developed. Eventually, the results of simulation prove the validity of the theorem, and demonstrate the synchronization phenomenon of coupled systems in different ways and for different systems.