Linearized stability in periodic functional differential equations with state-dependent delays

被引：60

作者：

Hartung, F ^{[1
]}

机构：

[1] Univ Veszprem, Dept Math & Comp, H-8201 Veszprem, Hungary

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2005年 / 174卷 / 02期

基金：

匈牙利科学研究基金会;

关键词：

linearization; state-dependent delay; stability; periodic solution;

D O I：

10.1016/j.cam.2004.04.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study stability of periodic solutions of a class of nonlinear functional differential equations (FDEs) with stare-dependent delays using the method of linearization. We show that a periodic solution of the nonlinear FDE is exponentially stable, if the zero solution of an associated linear periodic linear homogeneous FDE is exponentially stable. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：201 / 211

页数：11

共 21 条

[1] ANALYSIS OF A MODEL REPRESENTING STAGE-STRUCTURED POPULATION-GROWTH WITH STATE-DEPENDENT TIME-DELAY [J].

AIELLO, WG ;

FREEDMAN, HI ;

WU, J .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1992, 52 (03) :855-869

[2] A mathematical model of growth of population of fish in the larval stage: Density-dependence effects [J].

Arino, O ;

Hbid, ML ;

de la Parra, RB .

MATHEMATICAL BIOSCIENCES, 1998, 150 (01) :1-20

[3] LINEARIZING EQUATIONS WITH STATE-DEPENDENT DELAYS [J].

BROKATE, M ;

COLONIUS, F .

APPLIED MATHEMATICS AND OPTIMIZATION, 1990, 21 (01) :45-52

[4]

CAO Y, 1992, NONLINEAR ANAL-THEOR, V16, P95

[5] On the problem of linearization for state-dependent delay differential equations [J].

Cooke, KL ;

Huang, WZ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (05) :1417-1426

[6] Periodic solutions of differential equations with delay depending on solution [J].

Domoshnitsky, A ;

Drakhlin, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (05) :2665-2672

[7] On equations with delay depending on solution [J].

Domoshnitsky, A ;

Drakhlin, M ;

Litsyn, E .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 49 (05) :689-701

[8]

Gyori I., 2000, Acta Sci. Math, V66, P71

[9] On differentiability of solutions with respect to parameters in state-dependent delay equations [J].

Hartung, F ;

Turi, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 135 (02) :192-237

[10]

Hartung F., 2000, P C DYN SYST DIFF EQ, P416

← 1 2 3 →