The Number of Limit Cycles Bifurcating from a Quadratic Reversible Center

By using the first order Melnikov function method with multiple parameters presented in [Han & Xiong, 2014], we prove that 2[n+1/2 ] limit cycles can bifurcate from the quadratic reversible center (x) over dot = y(1 - x), (y) over dot = -x(1 - x) under nth degree polynomial perturbations for n >= 3. 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 n which is 4 (resp., n) when n = 2 (resp., n >= 3).