机械科学与技术2017，Vol.36Issue(9)：1340-1344,5.DOI:10.13433/j.cnki.1003-8728.2017.0905
双参数平面上Duffing系统TLE的计算与分岔分析
Calculating Top Lyapunov Exponent of Duffing System on Two-parameter Plane and Analyzing its Bifurcation
摘要
Abstract
The method of calculating the top Lyapunov exponent of a Duffing system in the multi-parameter space is given,and the distribution characteristic of the top Lyapunov exponent of the Duffing system in its two-parameter plane is calculated.Bifurcation characteristics of the Duffing system are discussed with the single parameter bifurcation diagram.The discussion results show that the Duffing system has various bifurcation curves including periodic jump,pitchfork bifurcation and period-doubling bifurcation in its two-parameter plane.The period-doubling bifurcation curve cycles constantly appear and nest each other,making the system finally evolve the chaotic state via period-doubling bifurcation sequences.These periodic bifurcation curves are truncated by the periodic jumping curve,making the system move into different periodic states via the cycle jump curve.The intersection of various bifurcation curves in the two-parameter plane makes the local bifurcation characteristic of the system become very complex.The calculation and analysis of the Duffing system prove that this method is effective and feasible in terms of computational chaos.关键词
Duffing系统/最大Lyapunov指数/双参数特性/分岔/周期跳跃Key words
Duffing system/top Lyapunov exponent/two-parameter plane/bifurcation/periodic jump分类
数理科学引用本文复制引用
张艳龙,石建飞,王丽..双参数平面上Duffing系统TLE的计算与分岔分析[J].机械科学与技术,2017,36(9):1340-1344,5.基金项目
国家自然科学基金项目(11302092,11362008)资助 （11302092,11362008）
