• 论文 •

### 一维向量场含时变参数的非完全分岔

1. 北京航空航天大学 理学院
• 收稿日期:1998-11-19 出版日期:2000-03-31 发布日期:2010-09-27
• 作者简介:化存才(1964-),男,云南玉溪人,博士生,100083,北京.
• 基金资助:

国家自然科学基金资助项目(19772007); 教育部博士点基金资助项目(98000619)

### Imperfect Bifurcation of One-Dimensional Vector Field with a Time-Dependent Parameter

HUA Cun-cai, LU Qi-shao, WANG Qi

1. Beijing University of Aeronautics and Astronautics,School of Science
• Received:1998-11-19 Online:2000-03-31 Published:2010-09-27

Abstract: A new and simple method is proposed for studying an imperfect bifurcation problem of one-dimensional vector field with a time-dependent parameter. A basic method of scaling balance is established. By combining this method with the continuity of the solutions of ordinary differential equations with respect to time and parameters, the delayed bifurcation transition and the influences on the bifurcation diagrams are discussed. Three different types of model bifurcation equations are analyzed concretely, the scaling relations and the intervals of bifurcation transition are given. The qualitative analysis results coincide with the numerical ones. Our studies imply that there exists a critical value of imperfect parameter such that if the imperfect parameter is respectively smaller than, equal to and larger than the critical value, the corresponding time dependent bifurcation is delayed, almost the same as and advanced the steady one respectively.