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In this paper we analyze the effect of a non-trivial topology on the dynamics of the so-called Naming Game, a recently introduced model which addresses the issue of how shared conventions emerge spontaneously in a population of agents. We consider in particular the small-world topology and study the convergence towards the global agreement as a function of the population size $N$ as well as of the parameter $p$ which sets the rate of rewiring leading to the small-world network. As long as $p gg 1/N$ there exists a crossover time scaling as $N/p^2$ which separates an early one-dimensional-like dynamics from a late stage mean-field-like behavior. At the beginning of the process, the local quasi one-dimensional topology induces a coarsening dynamics which allows for a minimization of the cognitive effort (memory) required to the agents. In the late stages, on the other hand, the mean-field like topology leads to a speed up of the convergence process with respect to the one-dimensional case.
We investigate the multifractals of the normalized first passage time on one-dimensional small-world network with both reflecting and absorbing barriers. The multifractals is estimated from the distribution of the normalized first passage time charac
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point re
The class of Koch fractals is one of the most interesting families of fractals, and the study of complex networks is a central issue in the scientific community. In this paper, inspired by the famous Koch fractals, we propose a mapping technique conv
A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with different shortcut densities $phi$ where $phi=0$ and $1$ represent a regular lattice and a random network respectively. In the small-world reg
We study the decay process for the reaction-diffusion process of three species on the small-world network. The decay process is manipulated from the deterministic rate equation of three species in the reaction-diffusion system. The particle density a