一类二次系统的全局结构

Global structure of a class of quadratic system

目的讨论一类二次系统极限环的惟一性及给出全局结构图。方法运用Lienard方程组理论及环域定理对此类二次系统极限环的惟一性进行讨论,并运用分支理论讨论异宿环的稳定性。结果得到了此类系统极限环的存在惟一性及不存在性和异宿环稳定及不稳定的完整结果。结论得到了一类二次系统极限环的惟一性,给出了参数取值不同时的7种全局结构图。

Aim In order to discuss the uniqueness of limit cycles for a class of quadratic system and draw the global structures. Methods Lienard＇s set of equations theory and ring domain thorem are applied to discuss the uniqueness of limit cycles for a class of quadratic system. And on the basis of the furcation theory, the stability on heteroclienic loop is to study. Results The existence, uniqueness and nonexistence of limit cycles are analyzed and discussed, and the stability and unstability on heteroclienic loop are analyzed and discussed. Conclusion The complete results on the existence and uniqueness of limit cycles are obtained and given seven kinds of global structures.