Self-organized criticality dynamic of forest fire model

Here, we focus on the self-organized dynamic. We propose an average forest density dynamical function (rho) over bar (t) in a two-dimensional Self-Organized Critical (SOC) forest fire model based on mean-field theory. We find that the average number of destroyed trees (S) over bar is dependent on both alpha (ratio of sparking frequency f over trees growth probability p) and system evolution time t. The result is well matched with the `"Yellowstone effect''. A transient cascade of burned trees from zero to small and large clusters at a critical density of trees q (rho) over bar and alpha is also discussed through computer simulation and mathematical analysis.