Degree-Biased Advection-Diffusion on undirected graphs/networks

Miranda, Manuel.; Estrada, Ernesto.
Mathematical Modelling of Natural Phenomena 17, 30 (2022)

There are several phenomena in nature governed by simultaneous or intermittent diffusion
and advection processes. Many of these systems are networked by their own nature. Here we propose
a degree-biased advection processes to undirected networks. For that purpose we define and study
the degree-biased advection operator. We then develop a degree-biased advection-diffusion equation
on networks and study its general properties. We give computational evidence of the utility of this
new model by studying random graphs as well as a real-life patched landscape network in southern
Madagascar. In the last case we show that the foraging movement of the species L. catta in this
environment occurs mainly in a diffusive way with important contributions of advective motions in
agreement with previous empirical observations.

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