Reaction-diffusion processes in scale-free networks

Lazaros K. Gallos; Panos Argyrakis

doi:10.1117/12.490200

7 May 2003 Reaction-diffusion processes in scale-free networks

Lazaros K. Gallos, Panos Argyrakis

Proceedings Volume 5114, Noise in Complex Systems and Stochastic Dynamics; (2003) https://doi.org/10.1117/12.490200
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States

Abstract

In this work we investigate the dynamics of reaction-diffusion processes on scale-free networks. Particles of two types, A and B, are randomly distributed on such a network and diffuse using random walk models by hopping to nearest neighbor nodes only. Here we treat the case where one species is immobile and the other is mobile. The immobile species acts as a trap, i.e. when particles of the other species encounter a trap node they are immediately annihilated. We numerically compute Φ(n,c), the survival probability of mobile species at time n, as a function of the concentration of trap nodes, c. We compare our results to the mean-field result (Rosenstock approximation), and the exact result for lattices of Donsker-Varadhan. We find that for high connectivity networks and high trap concentrations the mean-field result of a simple exponential decay is also valid here. But for low connectivity networks and low c the behavior is much more complicated. We explain these trends in terms of the number of sites visited, S(_n), the system size, and the concentration of traps.

Citation Download Citation

Lazaros K. Gallos and Panos Argyrakis "Reaction-diffusion processes in scale-free networks", Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); https://doi.org/10.1117/12.490200

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