Burger, Martin, Pietschmann, Jan-Frederik, Ranetbauer, Helene, Schmeiser, Christian and Wolfram, Marie-Therese (2022) Mean field models for segregation dynamics. European Journal of Applied Mathematics, 33 (1). pp. 111-132. doi:10.1017/S095679252000039X ISSN 0956-7925.
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Abstract
In this paper, we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well as the available space. All individuals have the tendency to stay within their own group and avoid the others. These interactions lead to the formation of aggregates in case of a single species and to segregation in the case of multiple species. We derive two different mean-field models, which are based on these interactions and weigh local and non-local effects differently. We discuss existence and stability properties of solutions for both models and illustrate the rich dynamics with numerical simulations.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Mean field theory, Differential equations, Partial, Dynamics, Boundary value problems |
| Journal or Publication Title: | European Journal of Applied Mathematics |
| Publisher: | Cambridge University Press |
| ISSN: | 0956-7925 |
| Official Date: | February 2022 |
| Dates: | Date Event February 2022 Published 23 December 2020 Available 4 January 2019 Accepted |
| Volume: | 33 |
| Number: | 1 |
| Page Range: | pp. 111-132 |
| DOI: | 10.1017/S095679252000039X |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Re-use Statement: | This article has been accepted for publication in a revised form for publication in European Journal of Applied Mathematics. Link to Journal’s site on cambridge.org. https://doi.org/10.1017/S095679252000039X |
| Access rights to Published version: | Restricted or Subscription Access |
| Copyright Holders: | © The Author(s), 2020. Published by Cambridge University Press |
| Date of first compliant deposit: | 10 January 2019 |
| Date of first compliant Open Access: | 23 June 2021 |
| RIOXX Funder/Project Grant: | Project/Grant ID RIOXX Funder Name Funder ID EP/P01240X/1 [EPSRC] Engineering and Physical Sciences Research Council |
| Related URLs: | |
| URI: | https://wrap.warwick.ac.uk/112594/ |
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