An impulsive predator-prey model of integrated pest management Hong Zhang Department of Mathematics, Jiangsu University, JiangSu, ZhenJiang 212013, P.R.China Paul Georgescu Department of Mathematics and Its Applications, Central European University, Nador u. 9, H-1051 Budapest, Hungary Department of Mathematics, “Gh. Asachi” Technical University of Ia¸ si, Bd. Copou 11, 700506 Ia¸ si, Romania Lansun Chen Department of Applied Mathematics, Dalian University of Technology, DaLian, LiaoNing 116024, P.R.China Abstract From a practical point of view, the most efficient strategy for pest control is to combine an array of techniques to control the wide variety of potential pests that may threaten crops in an ap- proach known as integrated pest management (IPM). In this paper, we propose a predator-prey (pest) model of IPM in which pests are impulsively controlled by means of spraying pesticides (the chemical control) and releasing natural predators (the biological control). It is assumed that the biological and chemical control are used with the same periodicity, but not simultane- ously. The functional response of the predator is allowed to be predator-dependent, in the form of a Beddington-DeAngelis functional response, rather than to have a perhaps more classical prey-only dependence. The local and global stability of the pest-eradication periodic solution, as well as the permanence of the system, are obtained under integral conditions which are shown to have biological significance. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations. Keywords Beddington-DeAngelis functional response, impulsive controls, stability analysis, pest-eradication periodic solution, permanence, fixed point approach, supercritical bifurcation, economic threshold. Preprint submitted to Elsevier 15 October 2007