一类时间离散反应扩散对流模型的全局动力学  

Global dynamics of a class of temporally-discrete reaction-diffusion-advection models

作　　者：彭清源 郭志明[1] PENG Qing-yuan;GUO Zhi-ming(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2024年第3期26-32,共7页Journal of Guangzhou University:Natural Science Edition

摘　　要：时间离散空间连续的反应扩散方程模型是描述物种扩散行为的一类重要的研究工具。考虑到物种除了随机扩散外还会存在依赖于局部环境的扩散,文章建立了单个物种关于时间离散空间连续的反应扩散对流模型,然后利用主特征值理论分析了模型平衡点的存在性和稳定性。研究表明,加入依赖于局部环境的扩散对种群的生存是有利的。The temporally-discrete and spatially-continuous reaction-diffusion model is one of the most important tools to describe diffusion behavior.In this paper,it is assumed that the diffusion of species depends not only on random diffusion but also on advection due to the local environment,a temporally-discrete and spatially-continuous reaction-diffusion-advection model is established.The stability and existence of the equilibrium point of this model is analyzed by principal eigenvalue theory.It shows that advection based on the local environment is beneficial for population survival.

关 键 词：时间离散 空间连续 反应扩散对流模型 稳定性 主特征值 

分 类 号：O175[理学—数学]