| 乔志琴,刘兴波,朱德明.具有三重零奇异的时滞微分方程的分支[J].数学年刊A辑,2010,31(1):59~70 |
| 具有三重零奇异的时滞微分方程的分支 |
| Bifurcation in Delay Differential Systems with Triple-Zero Singularity |
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| DOI： |
| 中文关键词: 三重零奇异 时滞微分方程 Takens-Bogdanoy分支 Hopf-zero分支 |
| 英文关键词:Triple-zero singularity Delay differential system Takens-Bogdanov bifurcation Hopf-zero bifurcation |
| 基金项目:国家自然科学基金，上海市重点学科建设基金(No.B407)资助的项目 |
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| 中文摘要: |
| 主要研究三重零奇异的判定和在Rn上零特征根对应的广义特征空间,利用中心流形简化和规范型计算得到参数时滞微分方程的简化形式,对应于文[A note on the triple zero linear degeneracy:Normal forms,dynamical and bifurcation behaviour of an unfolding.Int J Bifur and Chaos,2002,12:2799-2820]中的结果具体分析具有三重零奇异的参数时滞微分方程的分支行为,并给出一例子来阐述得到的结果. |
| 英文摘要: |
| The paper is devoted to the determination of triple-zero singularity and the generalized eigenspace associated with zero eigenvalues in Rn.A concrete reduced form for parameterized delay differential systems is obtained by using center manifold reduction and normal form calculation.The results given in[A note on the triple zero linear degeneracy:Normal forms,dynamical and bifurcation behaviour of an unfolding.Int J Bifur and Chaos,2002,12:2799-2820]are employed to analyze the bifurcation behavior of the parameterized delay differential system with triple-zero singularity in detail and an example is presented to illustrate the results. |
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