关于一类非多项式平面微分系统的极限环及分支问题(英文)

Limit cycle and bifurcation problem for a class of nonpolynomial planar differential systems

旨在讨论一类非多项式平面微分系统.通过使用Dulac准则和Bendixson准则获得极限环不存在性的充分条件,引入广义Lienard系统理论以研究极限环的存在性及稳定性,应用Hopf分岔理论证明自原点分岔出极限环的充分条件.此外,给出一个范例以验证分析和结果的有效性.

This paper aims to discuss a class of the nonpolynomial planar differ- ential systems. The Dulac criterion and the Bendixson criterion are used to obtain some sufficient conditions for the nonexistence of the limit cycle, and the theory of the generalized Lidnard system is introduced to investigate the existence and the stability of the limit cycle. The Hopf bifurcation theory is applied to prove some sufficient conditions for the bifurcating limit cycle from the origin. In addition, one typical example is given to verify the effectiveness of the analyses and results.