Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3

Abstract

In this article we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. Then the maximum number of limit cycles that bifurcate from these periodic orbits is 6 and it is reached.

Keywords

• Polynomial vector field
• limit cycle
• averaging method
• weight-homogeneous differential system