Local dynamics of an equation with a large state-dependent delay

被引：4

作者：

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

Kashchenko, S. A. ^{[1
,2
]}

机构：

[1] Yaroslavl State Univ, Yaroslavl 150000, Russia

[2] Natl Res Nucl Univ MEPhI, Moscow 115409, Russia

来源：

DOKLADY MATHEMATICS | 2015年 / 92卷 / 02期

关键词：

DOKLADY Mathematic; Local Dynamic; Critical Case; Negative Real Part; Nonlinear Parabolic Equation;

D O I：

10.1134/S1064562415050221

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The behavior of solutions to first- and second-order differential equations with a large state-dependent delay is analyzed in a neighborhood of equilibrium. In critical cases, it is shown that their behavior is determined by the global dynamics of a nonlinear parabolic equation with periodic or antiperiodic boundary conditions, which is known as a quasi-normal form. Asymptotic formulas are presented that relate the solutions of the quasi-normal form and the original equation.

引用

页码：581 / 584

页数：4

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