Catastrophic transitions in a forest-grassland ecosystem

The paper analyses catastrophic transitions in a forest-grassland ecosystem from a nonlinear dynamical point of view. Recently, forest-grassland ecosystems have been experimentally proved to be bistable systems and thus bistable dynamical vegetation models has been proposed in the literature. We consider in this paper a recently proposed mathematical model which includes in a dynamic way the human influence based on the rarity perception of the grass and the forest value. Bifurcation analysis, conducted with continuation technique, has been conducted to trace and analyse the steady state solutions of the ecosystem considering the parameter related to the human influence as bifurcation parameter. Multiplicility and bistability have been observed in a wide parameter range, which are mainly organized by multiple hysteresis and transcritical bifurcations. Catastrophic transitions are then observed both as consequence of parameter perturbations in correspondence of limit point bifurcations or as consequence of the state vector perturbations in the multistability parameter region.