Dynamics of a System of Two Equations with a Large Delay

被引：1

作者：

Kashchenko, S. A. ^{[1
]}

Tolbey, A. O. ^{[1
]}

机构：

[1] Demidov Yaroslavl State Univ, Reg Sci & Educ Math Ctr, Yaroslavl, Russia

来源：

DOKLADY MATHEMATICS | 2023年 / 108卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

dynamics; stability; delay; quasi-normal forms; singular perturbations;

D O I：

10.1134/S1064562423701259

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The local dynamics of systems of two equations with delay is considered. The main assumption is that the delay parameter is large enough. Critical cases in the problem of the stability of the equilibrium state are identified, and it is shown that they are of infinite dimension. Methods of infinite-dimensional normalization are used and further developed. The main result is the construction of special nonlinear boundary value problems that play the role of normal forms. Their nonlocal dynamics determine the behavior of all solutions of the original system in a neighborhood of the equilibrium state.

引用

页码：369 / 373

页数：5

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