论文标题
图形上的非局部跨交流系统：能量景观和动态
Nonlocal cross-interaction systems on graphs: Energy landscape and dynamics
论文作者
论文摘要
我们探讨了在有限图上非局部相互作用的两个模型的动力学行为和能量性能。作者最近在具有非线性迁移率的广义图上的非二次Finslerian梯度流中引入了该模型。在连续且本地的环境中，这类系统表现出多种模式，包括两种物种的混合，部分吞噬或相位分离。这项工作展示了这种丰富的行为如何延伸到图形结构。我们提供了分析和数值证据。
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.
