Global exponential stability of positive periodic solutions for a class of multiple species Gilpin-Ayala system with infinite distributed time delays

This paper is concerned with a class of multiple species Gilpin-Ayala system with infinity distributed time delays. By applying fixed-point index theory, we have established some new sufficient conditions to ensure the existence of positive periodic solutions. We also analyze the global exponential stability of positive periodic solution for this system by constructing appropriate Lyapunov functional and transform technique. As an application, an interesting example and its simulation are illustrated the effectiveness of our main results.