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.

Meeting Name

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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International Standard Serial Number (ISSN)


Document Type

Article - Conference proceedings

Document Version


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Publication Date

01 Jul 2015