Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems

In this paper,bifurcation of small amplitude limit cycles from the degenerate equilibrium of a three-dimensional system is investigated.Firstly,the method to calculate the focal values at nilpotent critical point on center manifold is discussed.Then an example is studied,by computing the quasi-Lyapunov constants,the existence of at least 4 limit cycles on the center manifold is proved.In terms of degenerate singularity in high-dimensional systems,our work is new.