Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect

被引：103

作者：

Guo, Shangjiang ^{[1
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 04期

关键词：

Reaction-diffusion; Nonlocal delay effect; Hopf bifurcation; Stability; HOPF-BIFURCATION; POPULATION-MODEL; DISTRIBUTED DELAY; TRAVELING-WAVES; EQUATION; SYSTEM;

D O I：

10.1016/j.jde.2015.03.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the existence, stability, and multiplicity of spatially nonhomogeneous steady-state solution and periodic solutions for a reaction-diffusion model with nonlocal delay effect and Dirichlet boundary condition are investigated by using Lyapunov-Schmidt reduction. Moreover, we illustrate our general results by applications to models with a single delay and one-dimensional spatial domain. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：1409 / 1448

页数：40

共 50 条

[1] Stability and Hopf Bifurcation in a Reaction-Diffusion Model with Chemotaxis and Nonlocal Delay Effect
Li, Dong
Guo, Shangjiang
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (04):
[2] Bifurcation in a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition
Guo, Shangjiang
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 289 : 236 - 278
[3] BIFURCATION ANALYSIS OF A SINGLE SPECIES REACTION-DIFFUSION MODEL WITH NONLOCAL DELAY
Zhou, Jun
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 57 (01) : 249 - 281
[4] Global stability of reaction-diffusion equation with nonlocal delay
Qiu, Huanhuan
Ren, Beijia
Zou, Rong
APPLIED MATHEMATICS LETTERS, 2025, 163
[5] Stability and Hopf bifurcation for a three-component reaction-diffusion population model with delay effect
Ma, Zhan-Ping
APPLIED MATHEMATICAL MODELLING, 2013, 37 (08) : 5984 - 6007
[6] Traveling wavefronts in a reaction-diffusion model with chemotaxis and nonlocal delay effect
Li, Dong
Guo, Shangjiang
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2019, 45 : 736 - 754
[7] Global stability of a reaction-diffusion predator-prey model with a nonlocal delay
Xu, Rui
Ma, Zhien
MATHEMATICAL AND COMPUTER MODELLING, 2009, 50 (1-2) : 194 - 206
[8] On the stability of reaction-diffusion models with nonlocal delay effect and nonlinear boundary condition
Guo, Shangjiang
Li, Shangzhi
APPLIED MATHEMATICS LETTERS, 2020, 103
[9] Properties of Hopf bifurcation to a reaction-diffusion population model with nonlocal delayed effect
Yan, Xiang-Ping
Zhang, Cun-Hua
JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 385 : 155 - 182
[10] Bifurcation and stability of a reaction-diffusion-advection model with nonlocal delay effect and nonlinear boundary condition
Li, Chaochao
Guo, Shangjiang
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2024, 78

← 1 2 3 4 5 →