Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradication periodic solution and the dominance of dynamic behavior are investigated. This indicates that the model with fixed moments has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaches the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. Numerical investigations imply that there are several different types of periodic solutions and their maximum amplitudes are always less than the given economic threshold. The results also show that the time series at which the IPM strategies are applied are quite complex, which means that the application and realization of IPM in practice are very difficult.
The Probabilistic Economic Injury Level: Incorporating Uncertainty into Pest Management Decision-Making
