基于正弦函数的多涡卷吸引子及其动力学分析

A Dynamic Analysis of Multi-Scroll Attractors Based on the Sinusoidal Function

在tang设计的一个利用简单的正弦函数生成多涡卷混沌吸引子模型的基础上,首先,对该系统进行了基本的动力学分析,即根据每个平衡点对应的Jacobian矩阵计算出的特征值判定平衡点的稳定性,并利用相空间容积变化率对系统的耗散性进行了分析。然后利用Lyapunov指数和维数以及庞加莱截面图对系统进行了数值仿真分析,探讨了不同的参数变化对系统基本动力学特性的影响,为合理地选取系统参数提供了理论依据。

Based on tang design of a multi-scroll chaotic attractor model using a simple sinusoidal function, firstly, a basic dynamic analysis has been carried out of the system, with the stability of the equilibrium point determined according to the eigenvalues calculated by Jacobian matrix corresponding to each equilibrium point, followed by an analysis of the dissipation of the system by using the phase space volume change rate. Secondly, a numerical simulation analysis of the system can be made by using Lyapunov exponent, dimension and Poincare section diagram, with a tentative inquiry into the influence of different parameters on the basic dynamic characteristics of the system, thus providing a theoretical basis for the reasonable selection of system parameters.