EXTINCTION AND PERSISTENCE IN A LOGISTIC MODEL WITH BIRTH AND HARVESTING IMPULSES

This paper deals with a diffusive logistic model with birth and harvesting impulses, where birth pulses are for increase of population in short time because of birth, and harvesting pulses are used to describe decrease of population by regular harvesting or interventions. Firstly, the principal eigenvalue depending the impulsive rates, which is regarded as a threshold value, is introduced and characterized. Secondly, the asymptotic behavior of population is fully investigated and the sufficient conditions for the solution to be extinct or persist are given. Our results show that the increase brought about by birth, the decrease caused by harvest, and the intervention timing all have an impact on the persistence of species.