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

主要研究三重零奇异的判定和在R^n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.

The paper is devoted to the determination of triple-zero singularity and the generalized eigenspace associated with zero eigenvalues in R^n. 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, 12：2799-28201 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.