Multiple limit cycles of some strongly nonlinear Liénard-Van der Pol oscillator
Multiple limit cycles of some strongly nonlinear Liénard-Van der Pol oscillator
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DOI：
10.1016/j.amc.2015.08.049
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发表时间：
2015-11
期刊：
影响因子：
--
通讯作者：
Xianbo Sun
中科院分区：
文献类型：
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作者：
Xianbo Sun
本文研究了一类Liénard-Van der Pol振子的极限环，当阻尼效应消失时，该系统有一个双同宿环和两个尖点环.利用Melnikov函数理论和分支理论，得到了系统在奇异圆和奇异中心附近的极限环及其分布，得到了极限环的个数，改进了最近关于这类系统分支极限环个数的下界的一些结果.
In this paper, we investigate limit cycles of some Liénard–Van der Pol oscillator; the system has a double homoclinic loop and two cuspidal loops if the damping effect has vanished. By the related Melnikov function theory and bifurcation theories, the limit cycles near the singular circle and center with their distribution are found. The number of limit cycles obtained also reveals that some recent results on the lower bounds of the maximal number of limit cycles bifurcated from this kind of systems can be improved.