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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stability and bifurcation in a single species with nonlinear boundary conditions
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by Shangjiang Guo
Proc. Amer. Math. Soc. 151 (2023), 2057-2071
DOI: https://doi.org/10.1090/proc/16274
Published electronically: February 28, 2023

Abstract:

A single-species model subject to nonlinear boundary conditions is investigated. Existence, nonexistence, and local/global asymptotical stability of positive steady-state solutions are shown to identify the ranges of parameters, the growth rate functions, and boundary reaction functions. In particular, we show that the model can have multiple equilibria and in some parameter ranges can support Allee effects.
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Bibliographic Information
  • Shangjiang Guo
  • Affiliation: School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, People’s Republic of China
  • MR Author ID: 679488
  • ORCID: 0000-0002-9114-5269
  • Email: guosj@cug.edu.cn
  • Received by editor(s): November 5, 2020
  • Received by editor(s) in revised form: April 3, 2021, April 21, 2021, August 3, 2021, and September 7, 2022
  • Published electronically: February 28, 2023
  • Additional Notes: This work was supported in part by the National Natural Science Foundation of P.R. China (Grant No. 12071446), and by the Fundamental Research Funds for the Central Universities, People’s Republic of China, China University of Geosciences (Wuhan) (Grant No. CUGST2).
  • Communicated by: Wenxian Shen
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2057-2071
  • MSC (2020): Primary 35B35, 35K57, 35Q92, 92D40
  • DOI: https://doi.org/10.1090/proc/16274
  • MathSciNet review: 4556200