Degree-Biased Advection-Diffusion on undirected graphs/networks

In Press.-- Pre-publication available at: https://hal.archives-ouvertes.fr/hal-03469355v2There 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.M.M. thanks financial support PRE2020-092875 by MCIN/AEI /10.13039/501100011033 and by FSE invierte en tu futuro. E.E. thanks Grant PID2019-107603GB-I00 by MCIN/ AEI /10.13039/501100011033.Peer reviewe