The Bifurcation of Limit Cycles for a Class of Z8- Equivariant Seventh Degree System

A class of Z8-equivariant seventh degree system is investigated and its first five order critical point values are given in personal computer.we discuss the bifurcation behavior of limit cycles,show that there are eight fine foci of five order and five limit cy-cles can bifurcate from each.So 40 small amplitude limit cycles can bifurcate from the seventh degree Z8-equivariant system under a certain condition.At the same time,the bifurcation condition and stability condition of limit cycles are obtained.