Dynamics of the burning model

Abstract

Abstract. We propose a new avalanching model which is characterized by a) a local threshold in the transition from passive to active states, b) finite life time of active sites, and c) is dissipative. This model seems to be more appropriate for the description of a continuous system where localized reconnection plays a crucial role. The model allows for an analytical treatment. We establish the shape of the distribution of cluster sizes and the relation of the observables to the model parameters. The results are illustrated with numerical simulations which support the analytical results.