4阶龙格库塔法和10阶连分式欧拉法 NonlinearDynamicsofDuffing

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  采用4阶龙格库塔法和10阶连分式欧拉法，数值计算、分析了分数阶阻尼Duffing系统的 动力学特性．利用相图、Poincare截面映射图和分岔图等非线性动力学分析方法研究了阻尼的分数 阶微积分阶数对Duffing系统动力学性能的影响，采用分岔图法研究了外部激励的幅值和频率变 化时分数阶阻尼Duffing系统的动力学行为．分析表明，分数阶阻尼的阶数在0．1～2．0发生变化 时，系统依次进入周期运动、混沌运动、周期运动、混沌运动和周期运动，并且在混沌运动区间中存 在着周期运动窗口，由周期运动进入混沌运动的倍周期过程比较明显，结果证实了阻尼的分数阶微 分阶数对系统的动力学特性影响比较大，因此在系统动力学设计和分析中应该重视．(Abstract：Nonlinear dynamics of Duffing system with fractional order damping is investigated。 The equations of fractional order damped Duffing system are established．The four-order Runge- Kutta method and ten-order CFE-Euler methods are performed tO solve the fractional order Duffing equations．The effects of fractional order on the system dynamics are proposed with phase di— agrams，bifurcation diagrams and Poincare map．The bifurcation diagram is utilized tO analyze the effect of excitation amplitude and frequency on Duffing system with fractional order damping． The analysis shows that the fractional order damped Duffing system exhibits period motion。cha— OS，period motion，chaos，period motion one by one when the fractional order change from 0．1 to 2．0．A period doubling route to chaos is appeared clearly．The numerical results verify the signif— icant effect of fractional order on system dynamics．It iS necessary to consider the fractional order of damping in the design and analysi)

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分数阶阻尼Duffing系统的非线性动力学特性.pdf,411178,2011-07-31