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Title: | Global dynamics of a two-species clustering model with Lotka–Volterra competition | Authors: | Tao, W Wang, ZA Yang, W |
Issue Date: | Jul-2024 | Source: | Nonlinear differential equations and applications : NoDEA, July 2024, v. 31, no. 4, 47 | Abstract: | This paper is concerned with the global dynamics of a two-species Grindrod clustering model with Lotka–Volterra competition. The model takes the advective flux to depend directly upon local population densities without requiring intermediate signals like attractants or repellents to form the aggregation so as to increase the chances of survival of individuals like human populations forming small nucleated settlements. By imposing appropriate boundary conditions, we establish the global boundedness of solutions in two-dimensional bounded domains. Moreover, we prove the global stability of spatially homogeneous steady states under appropriate conditions on system parameters, and show that the rate of convergence to the coexistence steady state is exponential while the rate of convergence to the competitive exclusion steady state is algebraic. | Keywords: | Boundedness Clustering model Global stability Lotka–Volterra competition Lyapunov functional |
Publisher: | Birkhaeuser Science | Journal: | Nonlinear differential equations and applications : NoDEA | ISSN: | 1021-9722 | EISSN: | 1420-9004 | DOI: | 10.1007/s00030-024-00934-7 | Rights: | © 2024 The Author(s) This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The following publication Tao, W., Wang, ZA. & Yang, W. Global dynamics of a two-species clustering model with Lotka–Volterra competition. Nonlinear Differ. Equ. Appl. 31, 47 (2024) is available at https://doi.org/10.1007/s00030-024-00934-7. |
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