Artículo de revista
Generalization of the Ehrenfest urn model to a complex network
Fecha
2015Registro en:
Physical Review E Volumen: 92 Número: 1 (2015)
DOI: 10.1103/PhysRevE.92.012103
Autor
Clark, Jaime
Kiwi Tichauer, Miguel
Torres Sánchez, Felipe
Rogan Castillo, José
Valdivia Hepp, Juan
Institución
Resumen
The Ehrenfest urn model is extended to a complex directed network, over which a conserved quantity is transported in a random fashion. The evolution of the conserved number of packets in each urn, or node of the network, is illustrated by means of a stochastic simulation. Using mean-field theory we were able to compute an approximation to the ensemble-average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the stochastic simulation. Using this analytic approximation we are able to find the asymptotic dynamical state of the system and the time scale to approach the equilibrium state, for different networks. The study is extended to large scale-free and small-world networks, in which the relevance of the connectivity distribution and the topology of the network for the distribution of time scales of the system is apparent. This analysis may contribute to the understanding of the transport properties in real networks subject to a perturbation, e.g., the asymptotic state and the time scale required to approach it.