Mean-field models for segregation dynamics

  • 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.

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Author:Martin Burger, Jan-Frederik PietschmannORCiDGND, Helene Ranetbauer, Christian Schmeiser, Marie-Therese Wolfram
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Parent Title (English):European Journal of Applied Mathematics
Publisher:Cambridge University Press (CUP)
Place of publication:Cambridge
Year of first Publication:2022
Release Date:2023/02/20
Tag:Applied Mathematics
First Page:111
Last Page:132
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme