Nonlocal cross-interaction systems on graphs: Energy landscape and dynamics
Analysis of PDEs
2022-04-21 v1
Abstract
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.
Cite
@article{arxiv.2204.09553,
title = {Nonlocal cross-interaction systems on graphs: Energy landscape and dynamics},
author = {Georg Heinze and Jan-Frederik Pietschmann and Markus Schmidtchen},
journal= {arXiv preprint arXiv:2204.09553},
year = {2022}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2107.11289