title: Propagation in a two-dimensional weighted local small-world network.
abstract: Propagation properties in a two-dimensional network with local small-world effects corresponding to the influence zone of each active site are studied. Two different weights based on characteristic times are introduced. The propagation of the front (here a forest fire front) in such a network exhibits two thresholds: the first one is geometrical corresponding to the percolation threshold and the second one is dynamical and results from the weighting procedure. The geometrical threshold is found to be a second-order phase transition as for regular networks. Further results are provided on the fractal dimension of the area covered during the propagation below the percolation threshold.
authors.affiliation: IUSTI/CNRS UMR 6595, Technopôle Château Gombert, Université de Provence, 5 rue Enrico Fermi, Marseille, France. zekri@univ-usto.dz
authors.forename: Nouredine
authors.initials: N
authors.lastname: Zekri
authors.forename: Bernard
authors.initials: B
authors.lastname: Porterie
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Clerc
authors.forename: Jean-Claude
authors.initials: JC
authors.lastname: Loraud