Pest Control Model With Delayed Stage Structure for Pest and Nonlinearly Impulsive Releasing Predator

Considering the low cost and minimal environmental impact, nonlinear impulsive biological control strategies are more consistent with the pest management. From this basic standpoint, we formulate a pest control model incorporating delayed stage structure for the pest population and nonlinear impulsive release of natural enemies, and then conduct a mathematical and ecological investigation. By comparison theorem of impulsive differential equations and some analysis methods of delay differential equations, the sufficient condition for the global attractivity of the pest-extinction periodic solution is obtained, and the threshold condition for the permanence of the system is given as well. Our mathematical results show that the maturation time delay for the pest and the nonlinear impulsive release of natural enemies play significant roles in governing the dynamics of the proposed system and the result of biological pest control. Model analysis also demonstrates that, when the mature pest populations are uniformly persistent, they can further be kept under the economic threshold level by controlling the crucial ecological parameters. Finally, our findings are illustrated through some numerical simulations.