Bistability in a model of grassland and forest transition

It is acknowledged that the role of fire and climate in determining savanna and forest distributions requires comprehensive theoretical reevaluation. In this paper, an ordinary differential equation model describing the grassland and forest transition is considered. We use a modified Hill function as the nonlinear response of fire frequency to grass abundance, and the global dynamics of the model is completely classified. It is shown that any solution converges to an equilibrium, and the system has one, two or three coexistence equilibria depending on parameter values. Our results provide precise parameter range of bistability.