PERSISTENCE AND EXTINCTION OF A PEST-NATURAL ENEMY DIFFUSIVE MODEL WITH BIRTH AND HARVESTING IMPULSES

To understand how birth pulses and human interventions jointly influence the spatial dynamics of pests and their natural enemies, this paper develops an impulsive reaction-diffusion model for a pest-natural enemy system. We first investigate the principal eigenvalue of a corresponding single-species eigenvalue problem using the Krein-Rutman theorem and establish its monotonicity with respect to impulse intensities. Based on these eigenvalues, we analyze the threshold dynamical behavior of the full model. Sufficient conditions for co-extinction, single-species persistence, and two-species coexistence are derived. Compared with existing impulsive models that focus on either single species or single impulsive event, our work explicitly couples birth pulses and harvesting impulses in a two-species reaction-diffusion framework. The eigenvalue-based threshold criteria extend the classical logistic impulsive theory to predator-prey interactions with spatial heterogeneity. Finally, numerical simulations are presented to illustrate the theoretical results and to explore the impact of birth pulses and human interventions on population dynamics.