  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.
