  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.
