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

Shanshan Chen; Jianshe Yu

doi:10.1016/j.jde.2015.08.038

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

Shanshan Chen
, Jianshe Yu^*

^*Corresponding author for this work

Guangzhou University
Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

60 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	218-240
Number of pages	23
Journal	Journal of Differential Equations
Volume	260
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2015.08.038
State	Published - 1 Jan 2016
Externally published	Yes

Keywords

Hopf bifurcation
Nonlocal delay
Reaction–diffusion equation
Stability

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10.1016/j.jde.2015.08.038

Cite this

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title = "Stability and bifurcations in a nonlocal delayed reaction–diffusion population model",

abstract = "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.",

keywords = "Hopf bifurcation, Nonlocal delay, Reaction–diffusion equation, Stability",

author = "Shanshan Chen and Jianshe Yu",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = jan,

day = "1",

doi = "10.1016/j.jde.2015.08.038",

language = "英语",

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T1 - Stability and bifurcations in a nonlocal delayed reaction–diffusion population model

AU - Chen, Shanshan

AU - Yu, Jianshe

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Hopf bifurcation

KW - Nonlocal delay

KW - Reaction–diffusion equation

KW - Stability

UR - https://www.scopus.com/pages/publications/84940971949

U2 - 10.1016/j.jde.2015.08.038

DO - 10.1016/j.jde.2015.08.038

M3 - 文章

AN - SCOPUS:84940971949

SN - 0022-0396

VL - 260

SP - 218

EP - 240

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

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

Abstract

Keywords

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