多吸引子共存现象的数值研究方法及其实现

Numerical Analysis Method for Investigating the Multiple Attractors Phenomenon and its Realization

将分岔分析与全局分析相结合,介绍一种研究非线性动力系统多吸引子共存现象的数值分析方法。它周期解、混沌解均可求解,低周期、高周期解枝均能跟踪;不仅能连续跟踪主要解枝,而且能在多吸引子共存的参数区段捕捉一些次要解枝,将多吸引子共存现象形象地呈现在分岔图上。相应的分析程序配备了较强的数据处理和图形分析功能,能方便地对分岔数据进行详细分析.还集成了频谱分析、稳定性分析、李雅谱诺夫指数分析、全局分析等功能,形成了一个方便快捷的多功能非线性动力学分析平台。在修正的Holmes-Duffing系统中的数值实践证明了方法及软件的先进性和有效性。

By combining the bifurcation analysis with the global analysis, a numerical method is proposed for the bifurcation and chaos analysis of nonlinear dynamic systems. The merit of the method is that it can obtain both the periodic and chaotic solutions, trace both lower and high periodic, main and subordinate solution branches, and it can show the coexisting phenomena of attractors on the bifurcation diagrams. The corresponding software is equipped with powerful functions of data processing and graphic analysis and the bifurcation diagrams can be analyzed easily and quickly in detail. The spectrum analysis, stability analysis, Lyapunov exponent analysis and global analysis based on point mapping are all integrated in the program. The effectiveness of the method and its software are illustrated by the numerical study of the modified Holmes-Duffing oscillator.