Nonlocal cross-interaction systems on graphs: energy landscape and dynamics

  • We explore the dynamical behavior and energetic properties of a model of two species that interact nonlocally on finite graphs. The authors recently introduced the model in the context of nonquadratic Finslerian gradient flows on generalized graphs featuring nonlinear mobilities. In a continuous and local setting, this class of systems exhibits a wide variety of patterns, including mixing of the two species, partial engulfment, or phase separation. This work showcases how this rich behavior carries over to the graph structure. We present analytical and numerical evidence thereof.

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Author:Georg Heinze, Jan-Frederik PietschmannGND, Markus Schmidtchen
Frontdoor URL
Parent Title (English):arXiv
Year of first Publication:2022
Release Date:2023/02/20
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme
Latest Publications (not yet published in print):Aktuelle Publikationen (noch nicht gedruckt erschienen)