Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations
Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations
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DOI：
10.1007/s10884-018-9642-6
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发表时间：
2017-10
影响因子：
1.3
通讯作者：
Xuemei Li;Zaijiu Shang
中科院分区：
文献类型：
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作者：
Xuemei Li;Zaijiu Shang
本工作重点研究具有椭圆型简并平衡点的常微分方程和时滞微分方程（简称 ODE 和 DDE）在准周期摄动下的准周期解的存在性。我们证明，在适当的假设下，大多数参数值的平衡点附近存在扰动 ODE 和 DDE 的准周期解，然后将这些结果应用于具有零 Hopf 奇点的延迟范德波尔振子。
This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that under appropriate hypotheses there exist quasi-periodic solutions for perturbed ODEs and DDEs near the equilibrium point for most parameter values, then apply these results to the delayed van der Pol’s oscillator with zero-Hopf singularity.