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Positive periodic solutions of discrete three-level food-chain model of Holling type II. (English) Zbl 1099.92079

Summary: With the help of differential equations with piecewise constant arguments, we first derive a discrete analogy of the 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.

MSC:

92D40 Ecology
39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)
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