Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

Mutualism is the interaction of two species of organisms that benefits both [1]. In general, mutualism may be either obligate or facultative. Obligatemutualistmay survive only by association, and facultative mutualist, while benefiting from the presence of each other, may also survive in the absence of any of them [2]. As it is well known, in recent years the nonautonomous and periodic population dynamical systems are extensively studied. The basic and important studied questions for these systems are the persistence, permanence, and extinction of species, global stability of systems and the existence of positive periodic solutions, positive almost periodic solutions and strictly positive solutions, and so forth. Many important and influential results have been established and can be found in many articles and books. Particularly, the existence of positive periodic solutions for various type population dynamical systems has been extensively studied in [1–16] and the references cited therein. In [7], the authors studied the following delayed twospecies model of facultative mutualism: