Achieving global convergence to an equilibrium population in predator–prey systems by the use of a discontinuous harvesting policy

This paper analyses the dynamics of two predator–prey models, namely, Lotka–Volterra and Leslie–Gower, when submitted to a specific harvesting schedule known as the weighted escapement policy. The main goal is to show that global stability of a desired equilibrium population can be achieved by the application of simple switching controls, chosen in accordance with variable structure system theory. A qualitative analysis shows that the global stability depends on the existence of virtual equilibrium points which in turn is ensured by a suitable choice of the control parameters.