Numerical simulation of particle circulation on a graph based on stochastic and deterministic models
Numerical simulation of particle circulation on a graph based on stochastic and deterministic models
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 23, 1, pp. 126-136 (2026)
Abstract:
A non-Markov stochastic model describing particle circulation on a two-vertex graph with two unidirectional edges is considered. Based on the analytical results and computational experiments, it is shown that the mathematical expectations of the number of particles at the vertices of the graph are described by a system of two linear differential equations with a constant delay.
Keywords: particle circulation on a graph, non-Markov random process, mathematical expectations, delay differential equations, Monte Carlo method.