Positive periodic solutions of discrete \(n\)-species food-chain systems. (English) Zbl 1087.39012

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.


39A11 Stability of difference equations (MSC2000)
92D25 Population dynamics (general)
Full Text: DOI


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