Periodic solutions of an n-species Lotka-Volterra type food-chain model with time delays

An n-species periodic Lotka-Volterra type simple food-chain model with time delays is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulations are presented to illustrate our main results.