Modelling and analysis of an impulsive SI model with Monod-Haldane functional response

An impulsive SI model with Monod-Haldane functional response for pest control is proposed and investigated. First, we have proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the above system can be permanent. Then, influences of impulsive perturbation including impulse period, the time of spraying pesticide and the quantity of releasing infective pests on the above system have been studied. Moreover, numerical simulations show that the system has rich dynamical behaviors. Finally, it is concluded that the approach of combining impulsive infective releasing with impulsive pesticide spraying is more effective than the classical one if the chemical control is adopted rationally.