一类三次系统的全局结构和分支

The global structure and bifurcation for a class of cubic system

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。

Aim To detailedly study some questions in uniqueness of limit cycles and quality of infinite critical point for a class of cubic system was written by XIE Xiang-dong and CHEN Feng-de （ Ann Diff Eqs, 2005,21（3）：474-479）. Metheds The both qualitative analysis and quanlititative analysis were used. Results The global structure and bifurcation of system i. e. x =-y＋ex＋lx^2＋mxy = P（x,y）,y=x（1＋ay＋by^2） = Q（x,y） were given. Conclusion That some global structures and bifurcation are new in cubic system.