一类E3^1系统的定性分析

The qualitative analysis of a class of E3^1 systems

目的研究一类三次系统的定性性质。方法利用定性理论并结合平面系统的分支理论。结果给出了原点O(0,0)为全局中心时的所有可能的全局结构和产生Hopf分支的充分条件。结论得到了关于此类三次系统的比较完整的结果。

Aim To research the qualitative property of a class of cubic system. Methods Using the qualitative theories and bifurcation theory of planar system. Results All the possible global structures are obtained when O （0, 0） is a center; meanwhile, the sufficient conditions for the system to generate the Hopfbifurcation are given. Condusion The relative systematic results on this class of cubic system are obtained.