Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

Details Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

2009-02-23

arxiv.org/abs/0902.3680v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

23 pages, 13 figures

Scientific paper

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits a surprisingly sharp phase transition which can be shifted by redefinition of neighbourhood. The results can also be interpreted in terms of disease-spreading and are quite unsettling from the epidemologist's point of view, since variation of one crucial parameter only by a few percent can result in the change from endemic to epidemic behaviour.

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