Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles

摘要

In this article, we study the limit cycles bifurcated from a Liénard system with a heteroclinic loop connecting two nilpotent saddles. We apply expansion theory of a first-order Melnikov function to investigate the number of limit cycles near the heteroclinic loop and the center, and by some perturbation theory we find 3 limit cycles with 7 different distributions. Last, the least upper bound of the number of limit cycles bifurcated from the annulus is given by an algebraic criterion developed in J. Differ. Equ. 251, 1656-1669 (2011).