Small-Amplitude Limit Cycles of Certain Planar Differential Systems

Abstract

In this work we consider the polynomial differential system $$\dot{x} = -y + x f(y)$$ , $$\dot{y} =x + y f(x)$$ , where f is a polynomial. This system is a certain generalization of the classical Lienard system. For that system, we solve the center problem for such family and compute the order of degeneracy of a weak focus for obtaining the maximum number of small-amplitude limit cycles.