ORIGINAL RESEARCH article
Front. Phys.
Sec. Social Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1657967
This article is part of the Research TopicInnovative Approaches to Pedestrian Dynamics: Experiments and Mathematical ModelsView all 6 articles
A NONLOCAL ADVECTION SYSTEM FOR TWO COMPETING SPECIES WITH RESOURCES RECOVERING TIME
Provisionally accepted
- 1University of Electronic Science and Technology of China School of Electronic Science and Engineering, Chengdu, China
- 2Tokyo Rika Daigaku - Oshamambe Campus, Oshamanbe, Japan
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Competitive interactions between multiple cell populations are crucial for modeling biological processes such as tumor growth and tissue regeneration. In this study, we investigate the nonlocal advection model for two-species competition, which characterizes cell growth and dispersion phenomena in co-culture experiments. To capture realistic phenomena in biology, we introduce the time delay representing population migration and resources recovering time. The primary objectives are to investigate the impact of time delays on competitive dynamics under various parameter settings and to develop numerical methods that ensure biological feasibility of solutions. Accordingly, we design a positivity-preserving finite volume scheme based on an upwind flux approach, guaranteeing non-negative population densities and discrete conservation properties. We examine the convergence orders of the scheme through the numerical experiments and explore the effects of time delays on species competition dynamics under different parameter settings.
Keywords: Two species model, Time delay, Hyperbolic PDE, Keller–Segel model, advection, Nonlocal
Received: 02 Jul 2025; Accepted: 19 Sep 2025.
Copyright: © 2025 Zeng, Enatsu and Zhou. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Yoichi Enatsu, yenatsu@rs.tus.ac.jp
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