To explore the impacts of regional evolution and impulses on the
persistence or extinction of species, a generalized logistic model with
impulses in an evolving domain is proposed and researched. Firstly, the
ecological reproduction index, which is regarded as a threshold value,
is introduced and characterized. Secondly, in the case of monotone or
non-monotone impulsive function, the asymptotic behavior of population
is fully investigated and the sufficient conditions for the solution to
persist, be extinct or blow up are given. Finally, numerical simulations
results indicate that whatever impulse is, larger periodic evolution
rates are more favorable for species. However, impulsive harvesting has
a negative impact on persistence of species, while birth pulse admits a
positive impact and even results in blowup.