The Number of Limit Cycles Bifurcating from a Quadratic Reversible Center

Abstract

By using the first order Melnikov function method with multiple parameters presented in [Han & Xiong, 2014], we prove that [Formula: see text] limit cycles can bifurcate from the quadratic reversible center [Formula: see text] under [Formula: see text]th degree polynomial perturbations for [Formula: see text]. Our result in this paper improves the existing lower bound on the maximal number of limit cycles bifurcating from quadratic reversible centers inside the polynomial differential systems of degree [Formula: see text] which is 4 (resp., [Formula: see text]) when [Formula: see text] (resp., [Formula: see text]).