ORIGINAL RESEARCH article
Front. Phys.
Sec. Social Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1657927
This article is part of the Research TopicInnovative Approaches to Pedestrian Dynamics: Experiments and Mathematical ModelsView all 7 articles
HYDRODYNAMIC CUCKER-SMALE MODEL WITH TIME DELAY AND OBSTACLE AVOIDANCE
Provisionally accepted
- 1University of Electronic Science and Technology of China, Chengdu, China
- 2Tokyo Rika Daigaku - Oshamambe Campus, Oshamanbe, Japan
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We study a hydrodynamic Cucker-Smale-type model incorporating both time delays and obstacle potentials. The model governs the evolution of velocity and density fields of the system, where delayed interactions drive alignment and obstacle potentials account for responses to obstacles or predators. We further extend the framework to two-species systems. To numerically solve the model, we design a high-order finite volume method based on a Lax--Friedrichs numerical flux with fifth-order weighted essentially non-oscillatory reconstruction and third-order Runge--Kutta time discretization, ensuring numerical stability and high-order accuracy. Numerical experiments confirm the stability and accuracy of the proposed scheme and illustrate how time delays and obstacle potentials, under specific communication kernels and initial conditions, affect the emergence of flocking or non-flocking behavior.
Keywords: Cucker–Smale model, time delays, Hyperbolic systems, Collectivebehavior, Flocking, obstacle avoidance
Received: 02 Jul 2025; Accepted: 22 Sep 2025.
Copyright: © 2025 Zheng, 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: Guanyu Zhou, wind_geno@live.com
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