On a nonlocal competition model in moving environment: The effects of impulsive interventions

Considering the long distance dispersal and human interventions on species, a free boundary problem for the competition model with nonlocal diffusion and periodic pulses is investigated. The principal eigenvalue of time-dependent eigenvalue problem, which depends on the length of habitat and impulsive intensity, is defined and analyzed. This index can be used to characterize the dynamics for three different competition cases: (a) invasive species is the inferior, (b) invasive species is the superior and (c) the competition is weak. Our results not only extend the existing ones for the cases without pulses, but also reveal that the introduction of human interventions makes the long time behaviors of competitors complex and diverse, and can alter the competition outcomes. In addition, whether the invasive species can eventually survive in the new environment depends not only on the imposed pulse, but also on the initial region and its own expanding capability in case (b).