Perturbation theory of the quadratic Lotka–Volterra double center

Abstract

We revisit the bifurcation theory of the Lotka–Volterra quadratic system [Formula: see text] with respect to arbitrary quadratic deformations. The system has a double center, which is moreover isochronous. We show that the deformed system can have at most two limit cycles on the finite plane, with possible distribution [Formula: see text], where [Formula: see text]. Our approach is based on the study of pairs of bifurcation functions associated to the centers, expressed in terms of iterated path integrals of length two.