Delay-induced instability in a reaction-diffusion model with a general advection term

Jie Liu; Shanshan Chen

doi:10.1016/j.jmaa.2022.126160

Delay-induced instability in a reaction-diffusion model with a general advection term

Jie Liu
, Shanshan Chen^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology
Harbin Institute of Technology Weihai

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

4 Scopus citations

Abstract

In this paper, we consider a delayed reaction-diffusion model with a general advection term. The stability/instability of the positive steady state and delay-induced Hopf bifurcation are investigated when the given parameter is near the principal eigenvalue of a non-self-adjoint elliptic operator. Moreover, some previous methods are improved to derive a priori estimates for the eigenvalue problem, which is crucial to show the existence of a Hopf bifurcation.

Original language	English
Article number	126160
Journal	Journal of Mathematical Analysis and Applications
Volume	512
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2022.126160
State	Published - 15 Aug 2022
Externally published	Yes

Keywords

Advection
Delay
Hopf bifurcation
Non-self-adjoint elliptic operator

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10.1016/j.jmaa.2022.126160

Cite this

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title = "Delay-induced instability in a reaction-diffusion model with a general advection term",

abstract = "In this paper, we consider a delayed reaction-diffusion model with a general advection term. The stability/instability of the positive steady state and delay-induced Hopf bifurcation are investigated when the given parameter is near the principal eigenvalue of a non-self-adjoint elliptic operator. Moreover, some previous methods are improved to derive a priori estimates for the eigenvalue problem, which is crucial to show the existence of a Hopf bifurcation.",

keywords = "Advection, Delay, Hopf bifurcation, Non-self-adjoint elliptic operator",

author = "Jie Liu and Shanshan Chen",

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AU - Chen, Shanshan

PY - 2022/8/15

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N2 - In this paper, we consider a delayed reaction-diffusion model with a general advection term. The stability/instability of the positive steady state and delay-induced Hopf bifurcation are investigated when the given parameter is near the principal eigenvalue of a non-self-adjoint elliptic operator. Moreover, some previous methods are improved to derive a priori estimates for the eigenvalue problem, which is crucial to show the existence of a Hopf bifurcation.

AB - In this paper, we consider a delayed reaction-diffusion model with a general advection term. The stability/instability of the positive steady state and delay-induced Hopf bifurcation are investigated when the given parameter is near the principal eigenvalue of a non-self-adjoint elliptic operator. Moreover, some previous methods are improved to derive a priori estimates for the eigenvalue problem, which is crucial to show the existence of a Hopf bifurcation.

KW - Advection

KW - Delay

KW - Hopf bifurcation

KW - Non-self-adjoint elliptic operator

UR - https://www.scopus.com/pages/publications/85126546663

U2 - 10.1016/j.jmaa.2022.126160

DO - 10.1016/j.jmaa.2022.126160

M3 - 文章

AN - SCOPUS:85126546663

SN - 0022-247X

VL - 512

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 126160

ER -

Delay-induced instability in a reaction-diffusion model with a general advection term

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Keywords

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