Rossler系统的动力学行为研究及混沌抑制

Study dynamics behavior for Rossler system and chaos control

研究了Rossler系统的动力学行为,用Lyapunov指数理论论证了该系统存在混沌现象,数值仿真的相图揭示了混沌现象存在的具体形式,全局分岔图显示了随着系统参数的变化,系统由周期轨道经倍化分岔序列通向混沌的动力学特性。系统随不同参数变化的分岔图表明:随着参数的变化,系统变化的趋势基本一致,只是系统参数变化的方向不同,系统变量的取值范围不同。利用比例微分控制器控制混沌,当控制参数取恰当数值时,该方法能将系统控制到期望的周期轨道。该文进一步完善了对Rossler系统动力学行为的研究,为该系统混沌行为的抑制及实际工程的应用提供了理论依据。

This paper studied the Rossler system dynamical behavior, with the Lyapunov index theory to prove the existence of chaotic phenomena, numerical simulation of phase diagrams reveal the chaotic phenomenon exists in specific forms, global bifurcation diagram shows along with the change of the system parameters, system have dynamic characteristics that from period track to the chaotic through doubling bi- furcation sequences. System with different parameters of the bifurcation diagram shows that ： when the pa- rameters change, the system have a similar change tendency, but the change of system parameters in dif- ferent directions, the system variable ranges are different. Using proportional and differential controller to control the chaos, when the control parameters is appropriate value, this method can be controlled system to the desired periodic orbit. The work to further improve study on dynamic behavior for Rossler system, for the chaotic behavior control and the practical application in engineering provides a theoretical basis.