周期驱动van der Pol-Duffing振荡器的周期运动

Yeyin Xu, A. Luo
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摘要

本文用半解析方法得到了周期驱动van der Pol-Duffing硬化振荡器在分岔树上的对称和非对称周期1运动。这种半解析方法发展了具有规定精度的隐式映射。在隐式映射的基础上,利用映射结构确定了van der Pol-Duffing振荡器的周期运动。通过鞍节点分岔确定周期1运动的对称性破缺,生成相应的非对称周期1运动。通过特征值分析确定了周期1运动的分岔性和稳定性。为了验证半解析解,还进行了数值模拟。
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On Periodic Motions in a Periodically Driven van der Pol-Duffing Oscillator
In this paper, the symmetric and asymmetric period-1 motions on the bifurcation tree are obtained for a periodically driven van der Pol-Duffing hardening oscillator through a semi-analytical method. Such a semi-analytical method develops an implicit mapping with prescribed accuracy. Based on the implicit mapping, the mapping structures are used to determine periodic motions in the van der Pol-Duffing oscillator. The symmetry breaks of period-1 motion are determined through saddle-node bifurcations, and the corresponding asymmetric period-1 motions are generated. The bifurcation and stability of period-1 motions are determined through eigenvalue analysis. To verify the semi-analytical solutions, numerical simulations are also carried out.
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