The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one (Q629239)

The authors consider a quadratic reversible Lotka-Volterra system of genus one that possesses a first integral with a center. As has been done by different authors, they investigate the cyclicity of the corresponding period annulus, i.e., the maximal number of limit cycles that emerge under arbitrary quadratic perturbations of the system. It is proved that the cyclicity is two, and that the period function of the center is strictly monotone. The proof utilizes standard tools in the field, such as the Picard-Fuchs equations for Abelian integrals, the Riccati equation for ratios of Abelian integrals, and their derivatives, rsp.