Bifurcation and stability of periodic solutions of Duffing equations
Bifurcation and stability of periodic solutions of Duffing equations
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DOI：
10.1088/0951-7715/21/11/001
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发表时间：
2008-11
期刊：
影响因子：
1.7
通讯作者：
Hongbin Chen;Yi A. Li
中科院分区：
文献类型：
--
作者：
Hongbin Chen;Yi A. Li
从全局分歧的角度研究了Duffing方程周期解的稳定性和精确多解性，证明了在强阻尼条件下，具有立方非线性项的Duffing方程最多存在三个T-周期解.更精确地说，我们证明了T-周期解形成一个光滑的S形曲线，每个T-周期解的稳定性是由Floquet理论决定的。
We study the stability and exact multiplicity of periodic solutions of the Duffing equation from the global bifurcation point of view and show that the Duffing equation with cubic nonlinearities has at most three T-periodic solutions under a strong damped condition. More precisely, we prove that the T-periodic solutions form a smooth S-shaped curve and the stability of each T-periodic solution is determined by Floquet theory.