ANALYSIS OF A DELAYED 2-STAGE POPULATION-MODEL WITH SPACE-LIMITED RECRUITMENT

In this paper we perform a global qualitative analysis of a delayed tw o-stage population model, which was proposed by Bence and Nisbet [Ecol ogy, 70 (1989), pp. 1434-1441] to study the dynamic behavior of open s ystems where older or larger individuals can inhibit the recruitment o f juveniles or smaller ones into the population, such as an open marin e population with space-limited recruitment. It is known that the time delay between settlement and recruitment into the adult population is a crucial factor needed to produce the observed cyclic fluctuations. In addition to showing that solutions with positive initial conditions are positive and bounded, we establish sufficient conditions for the (i) persistence of the system (the adult population eventually staying above a certain level); (ii) local stability and instability of the p ositive equilibrium; and (iii) global stability of the positive equili brium. Biological implications of these conditions are discussed.