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The Beverton–Holt Equation with Periodic Growth Rate

Martin Bohner, Sabrina Streipert

Abstract


In this paper, we study the Beverton–Holt difference equation with periodic carrying capacity and periodic inherent growth rate. For this equation, we present proofs of the first Cushing–Henson conjecture (there exists a unique periodic solution that is globally attractive) and the generalized second Cushing–Henson conjecture (the weighted average of the unique periodic solution is less than the weighted average of the carrying capacity).

Keywords


Beverton–Holt, periodic solution, Cushing–Henson conjecture, weighted Jensen inequality.

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