Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations

  • Xuemei LiEmail author
  • Zaijiu Shang


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.


Delay differential equation Degenerate equilibrium point Quasi-periodic solution Perturbation 


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Authors and Affiliations

  1. 1.Key Laboratory of High Performance Computing and Stochastic Information Processing, Department of MathematicsHunan Normal UniversityChangshaPeople’s Republic of China
  2. 2.HLM, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China

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