Stabilizing control of ratio-dependent predator-prey models

摘要

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. (c) 2005 Elsevier Ltd. All rights reserved.