InterJournal Complex Systems, 1463
Status: Accepted
Manuscript Number: [1463]
Submission Date: 2004
Simulation of random walks and reaction-diffusion processes on scale-free networks
Author(s): Lazaros Gallos ,Panos Argyrakis

Subject(s): CX.18



In this work we study diffusion properties on scale-free networks via Monte-Carlo simulations. We study some basic random walk properties taking place on a network substrate, including the mean squared displacement, the number of nodes visited and the survival probability of a random walker on a network with a concentration c of static traps. We find important deviations from the well-established classical diffusion solutions on lattice, where although the random walkers remain close to their origin, they can sample a large part of the network. For the trapping problem, we observe both mean-field and complicated behavior, depending on the connectivity of the network. We also report results on chemical reactions taking place on scale-free networks, based on the A+A and A+B models, where we show that a drastically different behavior arises as compared to the same reactions in normal spaces. The reactions proceed in an extremely rapid rate, where the concentration of the reactants reduces in a power-law form with an exponent higher than 1. The important effects of depletion zone generation (A+A) and segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead, we have observed clustering of A (A+A) and of mixed A and B (A+B) in the neighborhood of the hubs of the network. At the limit of very sparse networks the usual behavior is recovered.

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