Limit cycle containing nine critical points in its interior for a class of cubic systems

Abstract

Discuss a class of real planar cubic systems with a critical point O(0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O(0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.