title: Effect of threshold disorder on the quorum percolation model.
abstract: We study the modifications induced in the behavior of the quorum percolation model on neural networks with Gaussian in-degree by taking into account an uncorrelated Gaussian thresholds variability. We derive a mean-field approach and show its relevance by carrying out explicit Monte Carlo simulations. It turns out that such a disorder shifts the position of the percolation transition, impacts the size of the giant cluster, and can even destroy the transition. Moreover, we highlight the occurrence of disorder independent fixed points above the quorum critical value. The mean-field approach enables us to interpret these effects in terms of activation probability. A finite-size analysis enables us to show that the order parameter is weakly self-averaging with an exponent independent on the thresholds disorder. Last, we show that the effects of the thresholds and connectivity disorders cannot be easily discriminated from the measured averaged physical quantities.
authors: Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Denis Diderot-Paris 7, 10 rue A. Domon et L. Duquet, 75013 Paris Cedex, France.|Université d'Evry-Val d'Essonne, France.
authors: Pascal
authors: P
authors: Monceau
authors: Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Denis Diderot-Paris 7, 10 rue A. Domon et L. Duquet, 75013 Paris Cedex, France.
authors: Renaud
authors: R
authors: Renault
authors: Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Denis Diderot-Paris 7, 10 rue A. Domon et L. Duquet, 75013 Paris Cedex, France.
authors: Stéphane
authors: S
authors: Métens
authors: Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Denis Diderot-Paris 7, 10 rue A. Domon et L. Duquet, 75013 Paris Cedex, France.
authors: Samuel
authors: S
authors: Bottani