Extinction, persistence and growing in a degenerate logistic model with impulses

Abstract

This paper deals with an impulsive degenerate logistic model, where pulses are introduced for modeling interventions or disturbances, and degenerate logistic term may describe refugees or protections zones for the species. Firstly, the principal eigenvalue depending on impulse rate, which is regarded as a threshold value, is introduced and characterized. Secondly, the asymptotic behavior of the population is fully investigated and sufficient conditions for the species to be extinct, persist or grow unlimitedly are given. Our results extend those of well-understood logistic and Malthusian models. Finally, numerical simulations emphanzise our theoretical results highlighting that medium impulse rate is more favorable for species to persist, small rate results in extinction and large rate leads the species to an unlimited growth.