A class of quadratic reversible systems with a center of genus one

In this paper, we first investigate global phase portraits of a class of quadratic reversible systems with a center of genus one, and obtain six possible global phase portraits. We then perturb the phase portrait with a non-Morsean point, by using nth order polynomials, n=1,2,…,7. For the perturbed systems, we study the limit cycle bifurcation problem, obtaining some new results.