This paper studies a class of quartic system which is more general and realistic than the quartic accompanying system.x＇=-y＋ex＋lx^2＋mxy＋ny^2,y＇=x（1-Ay）（1＋Cy^2）,（＊）where C 〉 0. Sufficient conditions are obtained for the uniqueness of limit cycle of system （＊） and some more in-depth conclusion such as Hopf bifurcation.
目的研究谢向东,陈凤德的论文Uniqueness of limit cycles and quality of infinite criticalpoint for a class of cubic system(Ann Diff Eqs,2005,21(3):474-479)的遗留问题,是该文的继续。方法采用定性与定量的分析方法。结果完整给出了系统的全局结构和分支情况。结论说明该三次系统部分全局结构和分支情况在三次系统中还是首次发现。
