Positive periodic solutions of discrete \(n\)-species food-chain systems (Q2570714)

A speculative model of \(n\)-species closed food-chain systems is formulated in terms of an \(n\)-th order discrete system with discrete delays. The authors claim that such a formulation is more efficient than a continuous one in the case of non-overlapping generations. An extension theorem known already to Euler (attributed to two recent authors) plays a key role in proving that the proposed system may admit periodic solutions. The proof is non-constructive. No observational data are cited on any group of actual species. Their ecological niche is not even roughly described. The realism of the model is thus debatable.