Perturbations of May–Leonard system

In this paper we study the quadratic homogeneous perturbations of the 3-dimensional May–Leonard system with α+β=2α+β=2. It is shown that there are perturbed systems having exactly one or two limit cycles bifurcated from the periodic orbits of May–Leonard system. This is proved by estimating the number of zeros of the first and the second order Melnikov functions.