The Beverton-Holt q-Difference Equation with Periodic Growth Rate
In this paper, we study the Beverton-Holt equation with periodic inherent growth rate and periodic carrying capacity in the quantum calculus time setting. After a brief introduction to quantum calculus, we solve the Beverton-Holt q-difference equation using the logistic transformation. This leads to a linear q-difference equation where the solution is obtained using variation of parameters. The analysis of the solution aids our investigation of the first and second Cushing-Henson conjectures under the assumption of a periodic growth rate and a periodic carrying capacity. The first Cushing-Henson conjecture holds in the classical sense, which guarantees the existence of a unique periodic solution which is globally attractive. The analysis of the average of the unique periodic solution of the Beverton-Holt q-difference equation yields formulations of modified second Cushing-Henson conjectures.
M. Bohner and S. H. Streipert, "The Beverton-Holt q-Difference Equation with Periodic Growth Rate," Springer Proceedings in Mathematics and Statistics, vol. 150, pp. 3 - 14, Springer Verlag, Jul 2015.
The definitive version is available at https://doi.org/10.1007/978-3-319-24747-2_1
20th International Conference on Difference Equations and Applications, ICDEA 2014 (2014: Jul. 21-25, Wuhan, China)
Mathematics and Statistics
Keywords and Phrases
Calculations; Dynamical systems; Growth rate; Jensen inequality; Logistic transformation; Periodic solution; Q-difference equation; Quantum calculus; Variation of Parameters; Difference equations; Beverton-Holt; Cushing-Henson conjecture; Jensen inequality; Periodic solution; Quantum calculus
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Article - Conference proceedings
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01 Jul 2015