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。
The calculation of single parameter Top Lyapunov exponent is extended to the two-parameter plane,and the parameter regions of periodic motion,chaotic motion and bifurcation curves are obtained by calculating the Top Lyapunov exponent of Duffing system in two-parameter plane.Combining with the single-parameter bifurcation diagrams,phase diagrams and Poincarésection maps,the dynamic characters of system in two-parameter and the impact of damping coefficient a on two-parameter characters of system are discussed.Results obtained indicate that the complicated bifurcation curves of periodic jump,periodic-doubling bifurcation and pitchfork bifurcation of system take place in two-parameter plane,and the bifurcation curves continue to change with the increase of damping coefficient.Some special phenomenon,such as bifurcation curves intersect,nesting and evolution,that the system has not met in the past single-parameter bifurcation,are obtained.It can be concluded that the damping coefficient a has significant influence on dynamic character of system in two-parameter plane.Current research has some reference values for the study of the parameter coupling characteristics of other multi-parameter systems in engineering.
出处
《应用力学学报》
CSCD
北大核心
2017年第2期250-256,共7页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(11302092)
