变参数Lorenz系统的动力学特性研究

Study on Dynamics of the Varying Parameter Lorenz System

为了研究参数漂移对混沌系统的影响,对Lorenz系统的3个参数a、b和c分别施加正态随机扰动,数值计算变参数Lorenz系统的解和最大Lyapunov指数,研究系统参数受扰动的变参数Lorenz系统的动力学行为和混沌参数区域,并和固定参数Lorenz系统的混沌参数区域作比较.计算结果表明:对处于亚稳态、周期态的Lorenz系统施加一定的参数扰动,系统将产生混沌运动;变参数Lorenz系统的混沌参数区域比固定参数Lorenz系统的混沌参数区域更为广阔.文章提出的系统参数扰动法作为混沌反控制的一种新方法,能实现稳态系统的混沌化.

In order to study the influence of parameter shift on the chaotic system, normal random disturbance was applied to the parameters , and of Lorenz system respectively, and numerical solution and the Maximal Lyapunov exponent of this varying parameter Lorenz system were calculated. The behaviors and the chaotic region of varying parameter Lorenz system were investigated and the differences between varying parameter Lorenz system and the normal system with fixed parameters were later demonstrated. The results showed that the disturbance of parameters to Lorenz system which is originally in meta-stable or periodic states can generate chaos, and the chaotic region of varying parameter Lorenz system is much wider than the fixed parameter system. The system parameter perturbation method proposed in this paper is a new way for anti-chaos controlling that achieve chaos control of the stable system.