The dynamical behaviors of a Lotka–Volterra predator–prey model concerning integrated pest management

Abstract

According to the fact integrated pest management, a Lotka–Volterra predator-prey model with impulsive effect at fixed moment is proposed and investigated. We analyze such system from two cases: general case (taking IPM strategy) and special case (only choosing pesticides). In the first case, we show that there exists a globally asymptotically stable pest-eradication periodic solution when the period of impulsive effect is less than some critical value. The condition for the permanence is also given. By using bifurcation theory, we show the existence and stability of positive periodic solution when the pest-eradication lost its stability. In the second case, the system by only choosing chemical pesticides, we give the conditions of existence and stability of predator-free periodic solution. We obtain that the conditions for the permanence or extinction in the system we considered are quite different from the corresponding system without impulse. Finally, we compare validity of the IPM strategy with the classical methods (only biological control or chemical control), and conclude that IPM strategy is more effective than the classical one.