推广Sprott-Ⅰ系统的动力学分析与离散化实现

Dynamic Analysis and Discretization Implementation of Extension Sprott-Ⅰ System

在对基本Sprott-I混沌系统引入3个参数后,提出一种推广Sprott-I系统。系统具有一个不稳定平衡点,可以呈现出一个单涡卷混沌吸引子。通过不同参数的Lyapunov指数谱和分岔图数值仿真对系统进行了动力学分析。结果表明,其中一个参数的改变可以使系统从反向倍周期分岔通向混沌;而另外两个参数则都具有恒定的Lyapunov指数谱。进一步的理论分析则指出这两个参数还具有全局调幅特性和倒相控制作用。此外,在采用改进的Euler算法对系统进行离散化处理后,通过微控制器MSP430F249进行了相关的实验验证,从而证实了系统离散化实现的可行性。

By introducing three parameters to the basic Sprott-I system, an extension Sprott-I system is proposed in this paper. The system has one unstable equilibrium point, from which a single-scroll chaotic attractor can be evolved. The dynamic analysis for the system is carried out by the numerical simulation of Lyapunov exponent spectrum and bifurcation diagram to different parameters. The results show that the change to one of the parameters can lead the system to chaos by inverse period-doubling bifurcation, but the other two parameters can keep constant Lyapunov exponent spectrum. Further theoretical analysis indicates that the two parameters also have the characteristic of global amplitude modulation and the control function of phase inversion. Moreover, with discretization to the system by improved Euler algorithm, the correlative experimental verification is performed through microcontroller MSP430F249, thereby the feasibility of the discretization implementation to the system is proved.