用变量旋转变换实现声光双稳系统的混沌控制

设计了一种控制非线性系统混沌的变量旋转变换(VRT)方法。介绍了变量旋转变换方法的控制原理,并用此方法控制声光双稳(AOB)系统的混沌,以此验证其有效性。利用计算机仿真模拟了受控后声光双稳系统的动力学行为。模拟结果显示,旋转变换的关联系数cosθ,sinθ为系统的控制参数,通过恰当地选择旋转变换的关联系数,使受控后系统的李雅普诺夫(Lyapunov)指数λ由正值转变为负值,系统由混沌态转变为周期态,周期态不但有稳定的原系统存在的倍周期2np轨道,而且还有3mp,2n×3mp(n,m为整数)这样原系统以外的周期轨道。

Realization of Chaos Control in the Acousto-Optical Bistable System by the Variable Rotation Transformation

The variable rotation transformation (VRT) method is proposed to control nonlinear chaos system. Control principle is introduced,and acousto-optical bistable (AOB) system is taken as a typical example to demonstrate the effectiveness of this method. The dynamical behaviors of controlled AOB system are given by computer numerical simulation. The results show that the correlation coefficients cosθ, sinθ are system control parameters, the Lyapunov exponent λ of the system can be changed from the positive numerical value in the chaotic state into the negative numerical value in the periodic state by appropriately selecting correlation coefficients ,and the method not only can control the unstable periodic 2np orbits embedded in initial system to stable periodic orbits, but can control chaos system to other periodic 3mp and 2n×3mp (n,m are integers) orbits.