Work

Asymptotic Behavior of a Delayed Nonlocal Dispersal Lotka-volterra Competitive System

Year: 2025

Type: article

Abstract: This paper investigates the asymptotic behavior of a nonlocal dispersal Lotka-Volterra competitive system with time delay across the entire $\mathbb{R}^N$. We establish $L^\infty-$decay estimates of solutions of linear systems converging to equilibria utilizing the Fourier transform method applied to the fundamental solution and the Fourier splitting technique. For the nonlinear time-delayed nonlocal dispersal Lotka-Volterra competitive system, we leverage the results from linear systems and obtain the long-time behavior of solutions of the nonlinear system manifesting as the form of time-exponential. More precisely, we further deduce $L^\infty-$decay estimates of solutions of the original nonlinear system through the properties of convolution and Hölder inequality. Additionally, numerical simulations are presented to bolster the principal theoretical results and illustrate that the time delay impedes species growth.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240262

Authors: Yiming Tang, Xin Wu, Rong Yuan, Fengjie Geng, Zhaohai Ma

Institutions: China University of Geosciences (Beijing), East China Jiaotong University, Beijing Normal University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, China University of Geosciences, Beijing, China University of Geosciences, Division of Graduate Education

Award: G3108075664