Stability and bifurcations in a nonlocal delayed reaction-diffusion population model

被引：52
作者：
Chen, Shanshan [1 ,2 ]
Yu, Jianshe [1 ]
机构：
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
[2] Harbin Inst Technol, Dept Math, Weihai 264209, Shandong, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 01期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Reaction diffusion equation; Nonlocal delay; Hopf bifurcation; Stability; TRAVELING-WAVE FRONTS; HOPF-BIFURCATION; ASYMPTOTIC-BEHAVIOR; EQUATIONS; DYNAMICS; SYSTEMS;
D O I：
10.1016/j.jde.2015.08.038
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A nonlocal delayed reaction diffusion equation with Dirichlet boundary condition is considered in this paper. It is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium. The stability/instability of the bifurcated positive equilibrium and associated Hopf bifurcation are investigated, providing us with a complete picture of the dynamics. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：218 / 240
页数：23
相关论文
共 50 条
  • [31] 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
  • [32] Hepatitis C virus infection is blocked by HMGB1: A new nonlocal and time-delayed reaction-diffusion model
    Wang, Wei
    Ma, Wanbiao
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 320 : 633 - 653
  • [33] Stability and Hopf bifurcation of a delayed reaction-diffusion predator-prey model with anti-predator behaviour
    Liu, Jia
    Zhang, Xuebing
    NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2019, 24 (03): : 387 - 406
  • [34] Persistence of wavefronts in delayed nonlocal reaction-diffusion equations
    Ou, Chunhua
    Wu, Hanhong
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 235 (01) : 219 - 261
  • [35] Bifurcation analysis of reaction-diffusion Schnakenberg model
    Liu, Ping
    Shi, Junping
    Wang, Yuwen
    Feng, Xiuhong
    JOURNAL OF MATHEMATICAL CHEMISTRY, 2013, 51 (08) : 2001 - 2019
  • [36] Dynamics of a delayed reaction-diffusion predator-prey model with nonlocal competition and double Allee effect in prey
    Wang, Fatao
    Yang, Ruizhi
    INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2025, 18 (02)
  • [37] Stability Analysis of a Reaction-Diffusion Equation with Spatiotemporal Delay and Dirichlet Boundary Condition
    Chen, Shanshan
    Yu, Jianshe
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2016, 28 (3-4) : 857 - 866
  • [38] Stability and bifurcation analysis of a reaction-diffusion equation with spatio-temporal delay
    Zuo, Wenjie
    Song, Yongli
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 430 (01) : 243 - 261
  • [39] Global stability in a nonlocal reaction-diffusion equation
    Finkelshtein, Dmitri
    Kondratiev, Yuri
    Molchanov, Stanislav
    Tkachov, Pasha
    STOCHASTICS AND DYNAMICS, 2018, 18 (05)
  • [40] Stability of Traveling Wave Fronts for Nonlocal Delayed Reaction Diffusion Systems
    Lu, Guangying
    Wang, Xiaohuan
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2014, 33 (04): : 463 - 480
12345