Local bifurcations of critical periods for cubic Liénard equations with cubic damping

Continuing Chicone and Jacobs’ work for planar Hamiltonian systems of Newton’s type, in this paper we study the local bifurcation of critical periods near a nondegenerate center of the cubic Liénard equation with cubic damping and prove that at most 2 local critical periods can be produced from either a weak center of finite order or the linear isochronous center and that at most 1 local critical period can be produced from nonlinear isochronous centers.