Fokker-Planck equation on metric graphs
Jasur Matrasulov, Karimjon Sabirov
TL;DR
This paper studies the Fokker-Planck equation on metric graphs, providing exact solutions for various graph types and discussing applications to Brownian motion in networks.
Contribution
It introduces boundary conditions for the Fokker-Planck equation on metric graphs and derives exact solutions for star, tree, and loop graphs.
Findings
Exact solutions for star, tree, and loop graphs
Boundary conditions based on weight continuity and current conservation
Application insights for Brownian motion in networks
Abstract
We consider the Fokker-Planck equation on metric graphs. Vertex boundary conditions are imposed in the form of weight continuity and the probability current conservation. Exact solution of the is obtained for star, tree and loop graphs. Applications of the model to Brownian motion in networks and other problems are briefly discussed.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Complex Network Analysis Techniques · Theoretical and Computational Physics