一维空间中具有资源依赖扩散的单物种模型的渐近动力学

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中文摘要：本文研究一维空间中具有资源依赖扩散的单物种模型的渐近动力学.为了克服资源依赖扩散带来的分析困难,利用变量替换的思想将上述模型转变为一致扩散的模型.然后,采用夹挤方法获得模型正稳态解的存在唯一性,这个解在后面的分析中具有至关重要的作用.进一步,使用上下解方法得到模型解的渐近性行为.研究结果表明:在一维空间中,当时间趋向于无穷大时,模型解会局部一致地收敛到相应的正稳态解.

外文标题：Asymptotic Dynamics of a Single-species Model with Resource-dependent Dispersal in One Dimension

外文摘要：In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.

外文关键词：

Asymptotic dynamicsResource-dependent dispersalStationary solutionUpper-lower solutions method

作者：

黄赟、张大为

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作者单位：

仲恺农业工程学院数学与数据科学学院,广州,510225

佛山大学数学学院,佛山,528000

关键词：

渐近动力学资源依赖扩散稳态解上下解方法

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaGuangdong Basic and Applied Basic Research FoundationGuangdong Basic and Applied Basic Research Foundation

项目编号：

12301101121011212022A15151100192020A1515110585

出版年：

2024

DOI：

10.3969/j.issn.1006-8074.2024.03.002

数学理论与应用

湖南省数学学会

数学理论与应用

影响因子：0.281

ISSN：1006-8074

年,卷(期)：2024.44(3)