Degn-Harrison反应扩散系统的Turing不稳定性与Hopf分支  

Turing Instability and Hopf Bifurcation for the Degn-Harrison System with Reaction-diffusion

作　　者：李兵方[1] 郭改慧 李艳玲[3] LI Bing-fang;GUO Gai-hui;LI Yan-ling(Department of Basic Course,Shaanxi Railway Institute,Weinan 714000,China;School of Arts and Sciences,Shaanxi University of Science and Technology,Xi'an 710021,China;College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710119,China)

机构地区：[1]陕西铁路工程职业技术学院基础课部,陕西渭南714000 [2]陕西科技大学文理学院,陕西西安710021 [3]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《数学的实践与认识》2021年第7期219-225,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61872227,61672021);陕西高等教育教学改革研究一般资助项目(19BY053)。

摘　　要：在齐次Neumann边界条件下研究一类Degn-Harrison反应扩散系统.首先讨论常微分系统正平衡点的稳定性和Hopf分支,其次研究扩散系统,给出扩散系数对正平衡点稳定性的影响,建立系统的Turing不稳定性,同时在扩散系数满足一定条件时给出Hopf分支的存在性.The Degn-Harrison reaction-diffusion system subject to Neumann boundary conditions is considered.For the ODE system,the stability of the equilibrium is given.And then,the existence and stability of the Hopf bifurcation are obtained.For the PDE system with diffusion,the stability of the positive equilibrium and Turing instability caused by diffusion are given,and the existence of Hopf bifurcation is established depending on the diffusion coefficient.

关 键 词：Degn-Harrison反应扩散系统 HOPF分支 稳定性 

分 类 号：O175[理学—数学]