Quadratic perturbations of a class of quadratic reversible lotka-volterra systems

摘要

This paper is concerned with the bifurcation of limit cycles of a class of quadratic reversible Lotka-Volterra system $dot{z} = iz + z^{2} + bar{z}^{2}$ with b = -1/3. By using the Chebyshev criterion to study the number of zeros of Abelian integrals, we prove that this system has at most two limit cycles produced from the period annulus around the center under quadratic perturbations, which provide a positive answer for a case of the conjecture proposed by S. Gautier et al.