GLOBAL ASYMPTOTIC BEHAVIOR
AND DISPERSION IN AGE-STRUCTURED,
DISCRETE COMPETITIVE SYSTEMS

JOHN E. FRANKE AND ABDUL-AZIZ YAKUBU

Abstract. The model for this study is a two-species discrete competitive system with two age classes, juveniles and adults. As the juveniles of one of the species mature, they disperse between two patches. We provide sufficient conditions that guarantee global convergence to the extinction states of each of the two competing species. With an example, we illustrate that providing a safe refuge for an endangered species in an age-structured model could lead to the stable coexistence of all the competing species where there is extinction without the refuge. This shows that dispersal between patches could represent a powerful strategy for the long-run stable coexistence of competing species.
    Irrespective of initial population densities, we prove that an individual species with a sufficiently large carrying capacity persists in the age-structured model with patches.