Geodesic
Degree-biased advection–diffusion on undirected graphs/networks
Manuel Miranda1 ; Ernesto Estrada1
1 Institute of Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), 07122 Palma de Mallorca, Spain
Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 30.

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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 artificial 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.
DOI : 10.1051/mmnp/2022034

Manuel Miranda 1 ; Ernesto Estrada 1

1 Institute of Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), 07122 Palma de Mallorca, Spain 
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Manuel Miranda; Ernesto Estrada. Degree-biased advection–diffusion on undirected graphs/networks. Mathematical modelling of natural phenomena, Tome 17 (2022), article  no. 30. doi : 10.1051/mmnp/2022034. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2022034/

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