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
收藏
页码：581 / 584
页数：4
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