Qualitative analysis for a biological depletion model

作者：

Highlights：

• This paper is devoted to study the general depletion model.

• A better understanding of the existence and asymptotic stability of constant solutions is obtained.

• The difficulty lies in how to clarify the number and the region of constant solutions.

• The steady-state bifurcation from constant solutions is given.

• Numerical simulations are done to suggest that steady spike solutions may occur.

摘要

•This paper is devoted to study the general depletion model.•A better understanding of the existence and asymptotic stability of constant solutions is obtained.•The difficulty lies in how to clarify the number and the region of constant solutions.•The steady-state bifurcation from constant solutions is given.•Numerical simulations are done to suggest that steady spike solutions may occur.

论文关键词：Depletion model,Asymptotic stability,Bifurcation,Numerical simulation

论文评审过程：Received 25 July 2019, Revised 27 January 2021, Accepted 11 February 2021, Available online 26 February 2021, Version of Record 26 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126102