Title: A model for random fire induced tree-grass coexistence in savannas,
Abstract: Tree-grass coexistence in savanna ecosystems depends strongly on
environmental disturbances out of which crucial is fire. Most modeling attempts
in the literature lack stochastic approach to fire occurrences which is
essential to reflect their unpredictability. Existing models that actually
include stochasticity of fire are usually analyzed only numerically. We
introduce new minimalistic model of tree-grass coexistence where fires occur
according to stochastic process. We use the tools of linear semigroup theory to
provide more careful mathematical analysis of the model. Essentially we show
that there exists a unique stationary distribution of tree and grass biomasses.