Eur. Phys. J. B 76, 109-121 (2010)
https://doi.org/10.1140/epjb/e2010-00165-7

Steady-state dynamics of the forest fire model on complex networks

¹ Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
² Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Campus Nord, 08034 Barcelona, Spain

Corresponding author: ^a romualdo.pastor@upc.edu

Received: 11 November 2009
Revised: 19 April 2010
Published online: 4 June 2010

Abstract

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced by this topological fact. In this paper we consider a paradigmatic model of non-equilibrium dynamics, namely the forest fire model, whose relevance lies in its capacity to represent several epidemic processes in a general parametrization. We study the behavior of this model in complex networks by developing the corresponding heterogeneous mean-field theory and solving it in its steady state. We provide exact and approximate expressions for homogeneous networks and several instances of heterogeneous networks. A comparison of our analytical results with extensive numerical simulations allows to draw the region of the parameter space in which heterogeneous mean-field theory provides an accurate description of the dynamics, and enlights the limits of validity of the mean-field theory in situations where dynamical correlations become important.