Positive periodic solutions of discrete three-level food-chain model of Holling type II

With the help of differential equations with piecewise constant arguments, we first derive a discrete analogy of continuous three level food-chain model of Holling type II, which is governed by difference equations with periodic coefficients. A set of sufficient conditions is derived for the existence of positive periodic solutions with strictly positive components by using the continuation theorem in coincidence degree theory. Particularly, the upper and lower bounds of the periodic solutions are also established.