Duffing系统在双参数平面上的动力学特性分析

发布时间：2018-08-14 12:19

【摘要】：将单参数最大Lyapunov指数的计算推广到双参数平面上,数值计算Duffing系统在双参数平面上的最大Lyapunov指数,得到系统在参数平面上周期运动、混沌运动、各种分岔曲线的参数区域;结合系统单参数分岔图、相图、庞加莱截面图讨论了系统在参数平面上的分岔混沌过程以及阻尼系数对系统双参数特性的影响。结果表明:在双参数平面上系统出现了周期跳跃、周期倍化分岔、叉式分岔等复杂的分岔曲线,而且这些分岔曲线随阻尼系数的增加不断发生着复杂变化;得到系统在以往单参数分岔过程中很少出现的分岔曲线相交、嵌套、演变等特殊现象;阻尼系数对系统双参数耦合动力学特性有重要的影响。本文对工程中其它多参数系统的参数耦合特性的研究具有一定的参考价值。
[Abstract]:The calculation of the maximum Lyapunov exponent with one parameter is extended to the two parameter plane, and the maximum Lyapunov exponent of the Duffing system on the two parameter plane is numerically calculated. The parameter regions of the periodic motion, chaotic motion and various bifurcation curves of the system in the parameter plane are obtained. Based on the single-parameter bifurcation diagram, phase diagram and Poincare section diagram, the bifurcation chaos process of the system on the parametric plane and the influence of damping coefficient on the two-parameter characteristic of the system are discussed. The results show that there are complex bifurcation curves such as periodic jump, periodic doubling bifurcation and fork bifurcation on the two-parameter plane, and these bifurcation curves change with the increase of damping coefficient. Some special phenomena, such as intersection, nesting and evolution of bifurcation curves, which rarely occur in the process of single parameter bifurcation in the past, are obtained, and the damping coefficient has an important influence on the coupling dynamic characteristics of the system with two parameters. This paper has a certain reference value for the study of the parametric coupling characteristics of other multi-parameter systems in engineering.
【作者单位】：兰州交通大学机电工程学院;兰州城市学院数学学院;
【基金】：国家自然科学基金(11302092)
【分类号】：O175

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