Periodic solution for athree-species Lotka-Volterra food-chain model with time delays

A delayed three-species periodic Lotka-Volterra food-chain model without instantaneousnegative feedback is investigated. By using Gaines and Mawhinʹs continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness, and global stability of positive periodic solutions of the system. Computer simulations are presented to illustrate the conclusions.