Existence of Limit Cycles for a Class of Quartic Polynomial Differential System Depending on Parameters

Abstract

We studied the existence of limit cycles for the quartic polynomial differential systems depending on parameters. To prove that, first, we used the formal series method based on Poincare’ ideas to determine the center-focus. Then, by the Hopf bifurcation theory, we obtained the sufficient condition for the existence of the limit cycles. Finally, we provided some numerical examples for illustration.