Dirichlet 边界条件下的时滞合作-扩散-对流系统的稳定性与Hopf分支

数学理论与应用 ›› 2021, Vol. 41 ›› Issue (2): 28-.

Dirichlet 边界条件下的时滞合作-扩散-对流系统的稳定性与Hopf分支

李振振戴斌祥*

中南大学, 数学与统计学院，长沙，410083)

出版日期:2021-06-30 发布日期:2021-08-18

Stability and Hopf Bifurcation for a Delayed Cooperation-diffusion-advection System with Dirichlet Boundary Conditions

School of Mathematics and Statistics, Central South University, Changsha 410083, China

Online:2021-06-30 Published:2021-08-18
Contact: Corresponding author: Dai Binxiang(1962−), Male, Changsha, Hunan, Professor, PhD, 从事微分方程与动力系统研究；E−mail：bxdai@csu.edu.cn

摘要/Abstract

摘要： 本文研究一类具有Dirichlet边界条件的时滞合作-扩散-平流系统.我们首先讨论空间非齐次正稳态解的存在性和稳定性.其次，我们证明时滞的增加会使正稳态解失稳，并且当时滞值穿过临界分支点时系统会存在Hopf分支.

关键词: 合作-扩散-对流 , 稳定性 , Hopf分支

Abstract: This paper is devoted to a delayed cooperation-diffusion-advection system with Dirichlet boundary conditions. Firstly we discuss the existence and stability of the positive steady state. Secondly we show that an increasing delay will destabilize the positive steady state and lead to the occurrence of Hopf bifurcation when the delay crosses through the critical bifurcation points.

Key words: Cooperation-diffusion-advection , Stability , Hopf bifurcation

李振振戴斌祥. Dirichlet 边界条件下的时滞合作-扩散-对流系统的稳定性与Hopf分支[J]. 数学理论与应用, 2021, 41(2): 28-.