Persistence, extinction and blowup in a generalized logistic model with impulses and regional evolution

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.