Two non algebraic limit cycles of a class of polynomial differential systems with non-elementary equilibrium point

Abstract

Up to now, all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have one non algebraic limit cycle or two explicit limit cycles one is algebraic and another non-algebraic. In this paper we present a family of polynomial differential systems of degree 6k + 1 with k ∈ N∗, with non-elementary singular point. Under some suitable conditions, We show that our system exhibiting two non algebraic or two algebraic limit cycles explicitly given. And to illustrate our results we present some examples