Three Explicit Non-Algebraic Limit Cycles For A Class Of Polynomial Differential Systems

The existence of limit cycles is interesting and very important in applications. It is a key to understand the dynamic of polynomial differential systems. The aim of this paper is to investigate a class of planar differential systems of degree 6n + 1 where n is strictly positive integer. Under some suitable conditions, the existence of three non algebraic limit cycles or three algebraic limit cycles. Furthermore, these limit cycles are explicitly given in polar coordinates. Some examples are presented in order to illustrate the applicability of our results.