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The Beverton-Holt q-difference equation
Martin Bohner1, Rotchana Chieochan
1Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA. bohner@mst.edu
Abstract:
The Beverton-Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton-Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton-Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing-Henson conjectures.
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