Existence and Uniqueness of Asymptotically Periodic Solution for Cyclic System of Four Species Predator-Prey Equations

In the past decades, mathematical ecology, especially the study of dynamical properties occurring in the predator-pray system with delay there has seen much progress. Moreover, uniformly strong persistence of a non-linear asymptotically periodic.This paper is concerned with a cyclic predator-prey system with sigmoidal type functional responce. By constructing a suitable Lyapanov function, we obtain that the system has a unique asymptotically periodic solution which is globally asymptotically stable