Stabilizing control of ratio-dependent predator–prey models

In this paper, the control of a ratio-dependent predator–prey system is considered. This system, in its equivalent nondimensional form, is subjected to an on–off control, also known as a threshold policy. The control, applied only to the predator, is of the “constant effort removal” type. It is shown that such a control can be designed by a suitable choice of so called virtual equilibrium points. The analysis of the global stability of a specific nondimensional model is carried out. It shows that, in the nondimensional model, the on–off control changes the original equilibrium points on the axes to a globally stable positive equilibrium point, attained through a sliding mode, thus avoiding extinction, and achieving coexistence of both species.