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.
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.
出处
《数学理论与应用》
2024年第3期11-24,共14页
Mathematical Theory and Applications
基金
supported by the National Natural Science Foundation of China (Nos.12301101,12101121)
the Guangdong Basic and Applied Basic Research Foundation (Nos.2022A1515110019,2020A1515110585)。
