ESTIMATES OF PERIODS AND GLOBAL CONTINUA OF PERIODIC SOLUTIONS FOR STATE-DEPENDENT DELAY EQUATIONS

被引：10

作者：

Hu, Qingwen ^{[1
]}

Wu, Jianhong ^{[2
]}

Zou, Xingfu ^{[3
]}

机构：

[1] Univ Texas Dallas, Dept Math Sci, Richardson, TX 75080 USA

[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

[3] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2012年 / 44卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

state-dependent delay; Hopf bifurcation; analyticity; global continuation; slowly oscillating periodic solution; DIFFERENTIAL EQUATIONS; HOPF-BIFURCATION; EXISTENCE; FAMILIES; ORBITS; INDEX;

D O I：

10.1137/100793712

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the global Hopf bifurcation of periodic solutions for one-parameter systems of state-dependent delay differential equations, and specifically we obtain a priori estimates of the periods in terms of certain values of the state-dependent delay along continua of periodic solutions in the Fuller space C(R; RN+1) x R-2. We present an example of three-dimensional state-dependent delay differential equations to illustrate the general results.

引用

页码：2401 / 2427

页数：27

共 32 条

[1] GLOBAL BIFURCATIONS OF PERIODIC ORBITS [J].

ALEXANDER, JC ;

YORKE, JA .

AMERICAN JOURNAL OF MATHEMATICS, 1978, 100 (02) :263-292

[2] FAMILIES OF PERIODIC-ORBITS - VIRTUAL PERIODS AND GLOBAL CONTINUABILITY [J].

ALLIGOOD, KT ;

YORKE, JA .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1984, 55 (01) :59-71

[3]

[Anonymous], THESIS J LIEBIG U GI

[4]

[Anonymous], J DYNAMICS DIFFERENT

[5]

[Anonymous], 1979, COMMUN PART DIFF EQ

[6] Existence of periodic solutions for delay differential equations with state dependent delay [J].

Arino, O ;

Hadeler, KP ;

Hbid, ML .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 144 (02) :263-301

[7] 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

[8] On the existence and global bifurcation of periodic solutions to planar differential delay equations [J].

Baptistini, MZ ;

Taboas, PZ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 127 (02) :391-425

[9]

Chen Y., 2001, DIFFERENTIAL INTEGRA, V14, P1181

[10]

Chow S.-N., 1978, NONLINEAR ANAL, V2, P753

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