A competition model with impulsive interventions and environmental perturbations in moving environments

Abstract

In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment with upward or downward advection. The dependence of the principal eigenvalue of corresponding periodic impulsive eigenvalue problem on advection rates, habitat sizes and pulses is investigated, which gives precise conditions that classify the dynamics into four types of competition outcomes including coexistence, co-extinction, two different competition exclusions for small or negative advection rates. Some sufficient conditions on pulses or initial habitats for species spreading or vanishing, and spreading speeds are then established. Our results not only extend the existing ones to the case with pulses, but also reveal the effects of human and natural factors, that is, impulsive interventions factors including positive or negative impulsive effect, pulse intensity and timing can significantly affect and alter the competition outcomes. The different performances of the superior and inferior affected by environmental perturbations are also reflected in the simulations.