PACS. 87.23.Ge – Dynamics of social systems. PACS. 05.10.-a – Computational methods in statistical physics and nonlinear dynamics. PACS. 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion. Abstract. – We analyze the propagation of activity in a system of mobile automata. A number ρL d of elements move as random walkers on a lattice of dimension d, while with a small probability p they can jump to any empty site in the system. We show that this system behaves as a Dynamic Small World (DSW) and present analytic and numerical results for several quantities. Our analysis shows that the persistence time T ∗ (equivalent to the persistence size L ∗ of small-world networks) scales as T ∗ ∼ (ρp) −τ,withτ=1/(d+1). The network of collaboration of actors in movies, of world airports, or of neural connections in the worm Caenorhabditis elegans, can be represented in the formof a graph. Persons, airports, and neurons stand for the nodes of the network, and a bond is drawn when two actors are cast together in a film, when a non-stop flight exists between two airports, or when a neural connection is present, respectively [1, 2]. The relational graphs resulting fromthese
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Manrubia et al. (2001) studied this question.