Attenuation in the almost periodic Beverton-Holt equation

ABSTRACT

It is known that the Beverton-Holt equation with periodically varying carrying capacity has a globally attracting solution and the solution exhibits attenuation, i.e. the average of the solution over one period is strictly less than the average of the carrying capacity. Interpreted this means a periodically varying environment has a deleterious effect on the average of the solution. Also known is a randomly varying carrying capacity also yields attenuation. In this work the authors show that an almost periodic carrying capacity also yields attenuation.

KEYWORDS:

• Difference equation
• almost periodicity
• Beverton-Holt map
• attenuation
• ergodic
• discrete dynamics

AMS SUBJECT CLASSIFICATIONS:

• 39A30
• 92D25
• 92D40
• 37C75

Acknowledgements

The authors also thank the referee for helpful remarks.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

RJS is supported by a University of Southern California, Dornsife School of Letters Arts and Sciences Faculty Development Grant, 12-1855-0032.