Existence and Uniqueness of Limit Cycles for a Class of Normal Form Equations with Codimension Two Singularities

In this paper, the existence and uniqueness of limit cycles for a class of normal form equations with codimension two singularities are discussed. By transforming the equations into the generalized Liènard equation, we obtain the sufficient and necessary condition for existence of the unique limit cycle. And we simplify the proofs on uniqueness of limit cycles. In addition, the parameter conditions on existence of the unique limit cycle are given for a class of equations