Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations

摘要

This work focuses on the existence of quasi-periodic solutions for ordinaryand delay differential equations (ODEs and DDEs for short) with anelliptic-type degenerate equilibrium point under quasi-periodic perturbations.We prove that under appropriate hypotheses there exist quasi-periodic solutionsfor perturbed ODEs and DDEs near the equilibrium point for most parametervalues, then apply these results to the delayed van der Pol's oscillator withzero-Hopf singularity.