Global stability and the Hopf bifurcation for some class of delay differential equation

被引：11

作者：

Bodnar, Marek ^{[1
]}

Forys, Urszula ^{[1
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Inst Appl Math & Mech, PL-02097 Warsaw, Poland

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2008年 / 31卷 / 10期

关键词：

global stability; delay differential equation; Hopf bifurcation; unimodal function;

D O I：

10.1002/mma.965

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right-hand side depending only on the past. We extend the results from paper by U. Forys (Appl. Math. Gett. 2004; 17(5):581-584), where the right-hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright (C) 2007 John Wiley & Sons, Ltd.

引用

页码：1197 / 1207

页数：11

共 50 条

[1] Hopf Bifurcation for a Class of Partial Differential Equation with Delay
Azevedo, Katia A. G.
Ladeira, Luiz A. C.
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2004, 47 (03): : 395 - 422
[2] Hopf bifurcation and stability analysis of a delay differential equation model for biodegradation of a class of microcystins
Zhao, Luyao
Li, Mou
Ma, Wanbiao
AIMS MATHEMATICS, 2024, 9 (07): : 18440 - 18474
[3] Local and global Hopf bifurcation in a scalar delay differential equation
Giannakopoulos, F
Zapp, A
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 237 (02) : 425 - 450
[4] Stability and Hopf Bifurcation Analysis for Functional Differential Equation with Distributed Delay
Yuan, Yuan
Belair, Jacques
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2011, 10 (02): : 551 - 581
[5] Stability and Global Hopf Bifurcation of a class of Neural Network Model with Delay
Wang, Xiaojia
Yang, Shanlin
2011 7TH INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS, NETWORKING AND MOBILE COMPUTING (WICOM), 2011,
[6] Stability and Hopf bifurcation in a class of nonlocal delay differential equation with the zero-flux boundary condition
Hu, Wenjie
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (12) : 4184 - 4196
[7] Hopf Bifurcation of a Positive Feedback Delay Differential Equation
陈玉明
黄立宏
NortheasternMathematicalJournal, 2003, (03) : 213 - 223
[8] Hopf bifurcation for a class of fractional differential equations with delay
Babakhani, Azizollah
Baleanu, Dumitru
Khanbabaie, Reza
NONLINEAR DYNAMICS, 2012, 69 (03) : 721 - 729
[9] Hopf bifurcation for a class of fractional differential equations with delay
Azizollah Babakhani
Dumitru Baleanu
Reza Khanbabaie
Nonlinear Dynamics, 2012, 69 : 721 - 729
[10] Numerical Hopf bifurcation for a class of delay differential equations
Wulf, V
Ford, NJ
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 115 (1-2) : 601 - 616

← 1 2 3 4 5 →