Global positive periodic solutions of periodic \(n\)-species competition systems (Q1023023)

Lotka-Volterra systems have been investigated extensively for the last decades. Many results dealing with the global existence and attractivity of periodic solutions have been obtained. As an extension of the Lotka-Volterra models in 1973, a more complicated model was proposed by Gilpin and Ayala. In the presented paper, an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized \(n\)-species systems of Lotka-Volterra type and Gilpin-Ayala type is obtained. It improves a series of well-known sufficiency conditions in the literature about the problems mentioned above. The method is based on a fixed point theorem in a cone of a Banach space. This approach can be applied to more general competition systems