| 一类滞时微分方程的Hopf分歧 |
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| 引用本文： | 朱海龙,沈建,杨忠华.一类滞时微分方程的Hopf分歧[J].上海师范大学学报(自然科学版),2006,35(6):9-17. |
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| 作者姓名： | 朱海龙 沈建 杨忠华 |
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| 作者单位： | 上海师范大学,数理信息学院,上海,200234 |
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| 基金项目： | 国家自然科学基金;上海市教委资助项目;上海市重点学科建设项目;上海市科技发展基金 |
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| 摘 要： | 应用Liapunov-Schmidt约化方法，研究了一类滞时微分方程的Hopf分歧问题，在Hopf分歧点的附近，给出了周期解枝的近似解析表达式，同时用Liapunov-Schmidt约化方法结合分片Hermite插值多项式的配置法求解了Hopf分歧点附近的周期解枝，发现理论分析结果和数值结果吻合，证实了用Liapunov-Schmidt约化方法求解滞时微分方程周期解的有效性与可行性．
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| 关 键 词： | 滞时微分方程 Hopf分歧 Liapunov-Schmidt约化 周期解 |
| 文章编号： | 1000-5137（2006）064）009-09 |
| 收稿时间： | 2006-09-06 |
| 修稿时间： | 2006-09-06 |
Hopf bifurcation analysis of a class of delayed equation |
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| ZHU Hai-long,SHEN Jian,YANG Zhong-hua.Hopf bifurcation analysis of a class of delayed equation[J].Journal of Shanghai Normal University(Natural Sciences),2006,35(6):9-17. |
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| Authors: | ZHU Hai-long SHEN Jian YANG Zhong-hua |
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| Institution: | Mathmatics and Sciences College, Shanghai Normal University, Shanghai 200234, China |
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| Abstract: | Using the Liapunov-Schmidt reduction,we investigate the Hopf bifurcation of a class of delayed differential equations. Near the Hopf bifurcation point,we obtain the periodic solution branch bifurcated from the trivial solution. An approximate analytic expression of the periodic solution is given to compare with the numerical results, which are computed by the collocation method based on piesewise Hermite polynomials. The fact that the approximate analytic periodic solution nearly coincides with the numerical results shows the effectiveness of our analysis. |
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| Keywords: | delayed differential equation Hopf bifurcation Liapunov-Schmidt reduction periodic solution |
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