陆炳新,罗定军.二次系统(Ⅲ)n=0的极限环问题[J].数学研究及应用,2006,26(1):111~120 |
二次系统(Ⅲ)n=0的极限环问题 |
Limit Cycle Problem of Quadratic System (Ⅲ)n=0 |
投稿时间:2004-02-20 |
DOI:10.3770/j.issn:1000-341X.2006.01.019 |
中文关键词: 二次系统 Hopf分支 极限环. |
英文关键词:quadratic system Hopf bifurcation limit cycle. |
基金项目:国家自然科学基金(19871041) |
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中文摘要: |
本文研究了二次系统(Ⅲ)$_{n=0}$的极限环问题,利用Hopf分支理论,先考察其产生极限环的参数区域,对此外的参数区域,则运用定性分析的方法,分别给出了无环性的证明,并结合文[2]中的一个重要猜测进行讨论,完善了谢文$^{[5]}$的结论. |
英文摘要: |
The limit cycle problem of quadratic system $($Ⅲ$)_{n=0}$ is studied in this paper. By using Hopf bifurcation, the parameter regions for which limit cycles exist are obtained, and for the rest regions of parameters, the nonexistance of limit cycles is proved by using qualitative methods. A positive answer for an important conjecture in [2, \S9] is also given and it is shown that our results are more complete than that obtained in paper [5]. |
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