Limit cycles bifurcating from the periodic annulus of cubic homogeneous polynomial centers

Abstract

We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of any cubic homogeneous polynomial center when it is perturbed inside the class of all polynomial differential systems of degree n.

Keywords

• Polinomial vector field
• limit cycle
• averaging method
• periodic orbit
• isochronous center
• homogeneous cubic centers