Analyzing a generalized pest-natural enemy model with nonlinear impulsive control

Due to resource limitation, nonlinear impulsive control tactics related to integrated pest management have been proposed in a generalized pest-natural enemy model, which allows us to address the effects of nonlinear pulse control on the dynamics and successful pest control. The threshold conditions for the existence and global stability of pest-free periodic solution are provided by Floquet theorem and analytic methods. The existence of a nontrivial periodic solution is confirmed by showing the existence of nontrivial fixed point of the stroboscopic mapping determined by time snapshot, which equals to the common impulsive period. In order to address the applications of generalized results and to reveal how the nonlinear impulses affect the successful pest control, as an example the model with Hotting II functional response function is investigated carefully. The main results reveal that the pest free periodic solution and a stable interior positive periodic solution can coexist for a wide range of parameters, which indicates that the local stability does not imply the global stability of the pest free periodic solution when nonlinear impulsive control is considered, and consequently the resource limitation (i.e. nonlinear control) may result in difficulties for successful pest control.