Dynamical stabilization of grazing systems: An interplay among plant–water interaction, overgrazing and a threshold management policy

In a plant–herbivore system, a management strategy called threshold policy is proposed to control grazing intensity where the vegetation dynamics is described by a plant–water interaction model. It is shown that this policy can lead the vegetation density to a previously chosen level under an overgrazing regime. This result is obtained despite both the potential occurrence of vegetation collapse due to overgrazing and the possibility of complex dynamics sensitive to vegetation initial densities and parameter uncertainties.