Dynamics of a discontinuous discrete Beverton–Holt model

Abstract

Our aim is to investigate the global asymptotic behaviour, oscillation, periodicity and bifurcation in discontinuous Beverton–Holt type difference equation

where x₀>0, functions k and r are discontinuous piecewise constant functions

satisfying

and h is Heaviside function.

Keywords::

• oscillation
• semi-cycles
• periodicity
• discontinuous map
• bifurcation
• Beverton–Holt model

AMS Subject Classification::

• 39A11

Acknowledgement

Thanks to anonymous referees and Professor Candace M. Kent, for making valuable comments that are incorporated in the final version of the paper.

Notes

^1. Email: [email protected].