The dynamics of a predator-prey model with Ivlev's functional response concerning integrated pest management

A mathematical model of a predator-prey model with Ivlev's functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one. © Springer-Verlag 2004.