GLOBAL STABILITY IN A DIFFUSIVE
STAGE-STRUCTURED POPULATION SYSTEM
WITH TWO TIME DELAYS

H.I. FREEDMAN AND QIU-LIANG PENG

Abstract. In the present paper we consider a reaction-diffusion stage-structured population system with two time delays. We prove that the positive steady state is unique and globally asymptotically stable with respect to all positive solutions. This property implies that in this kind of system, the diffusion does not change the stability. However, we also prove that the effects of diffusion benefit the survival of populations. All these results have reasonable implications for real populations.