应用数学和力学2018，Vol.39Issue(3)：324-333,10.DOI:10.21656/1000-0887.380089
Duffing系统在双参数平面上的分岔演化过程
Bifurcation Evolution of Duffing Systems on 2-Parameter Planes
摘要
Abstract
The calculation method for the top Lyapunov exponents in the parameter space was given.The top Lyapunov exponents of Dufffmg systems on 2-parameter planes were calculated with the numerical method.Combined with the single-parameter top Lyapunov exponents,the bifurcation diagrams,the phase diagrams and the time response diagrams,the bifurcation and the bifurcation evolution process of Duffing systems on the 2-parameter planes were discussed in view of the change of system parameters.The results show that 2 different regions with the phenomena of missing edges appear when the pitchfork bifurcation occurs.The system has strong sensitivity to initial values in the regions where 2 attractors coexist.The system vibration amplitude decreases suddenly when the system moves through the period jump curve.The system flutter motion often occurs when the excitation frequency is relatively small.In addition,when the stiffness coefficient increases,the period-doubling bifurcation curve cycles constantly exist and nest each other in the 2 regions with the phenomena of missing edges,which makes the system finally evolve into a chaotic state via the period-doubling bifurcation sequences.The dynamic properties of the system are very complex on 2-parameter planes with the change of control parameters.关键词
Duffing系统/Lyapunov指数/双参数特性/分岔/周期跳跃Key words
Duffing system/Lyapunov exponent/2-parameter characteristic/bifurcation/periodic jump分类
数理科学引用本文复制引用
张艳龙,王丽,石建飞..Duffing系统在双参数平面上的分岔演化过程[J].应用数学和力学,2018,39(3):324-333,10.基金项目
国家自然科学基金(11302092 （）
11362008)The National Natural Science Foundation of China(11302092 （）
11362008) （）
