Lorenz系统的混沌同步控制及计算机仿真

Synchronous Control in Chaotic Systems of Lorenz and the Computer Simulation

针对Lorenz系统提出了以一定的耦合比例系数,实现主动系统和被动系统的同步控制以及计算机仿真。计算机仿真结果表明:在控制的过程中,控制周期随着松弛系数值的增大而减小,较大的松弛系数导致较快的控制。这个控制法则来源于李雅普诺夫稳定性原理,可以用来控制非同步系统达到同步,最终实现所要求的P-同步,即通过加入微小的控制可以在短时间内按任意比例系数实现对主动系统的响应的放大或缩小。数值仿真结果证实了所提新方法的有效性,并且可以按照实际需要的耦合比例实现同步控制。

Synchronous control of the master system and slave systems for the system of Lorenz and computer numerical simulation are realized in this paper. The computer numerical simulation shows that the transient period of control is generally reduced with an increase of the value of the slack constant. Clearly, the larger slack constant leads to higher convergence rate in the control. The control law is derived from Lyapunov stability theory. This control method could be employed to make a nonsynchronous system be synchronized, and manipulate the ultimate state of projective synchronization to any desired ratio. It allows us to use tiny control inputs to amplify or reduce the response of the driven system to any scale in a short transient period. The numerical simulation result confirms the effectiveness of the new method, and the method can realize the synchronous control according to the coupling ratio of demand.