Stochastic modified Beverton–Holt model with Allee effect II: the Cushing–Henson conjecture

Abstract

We consider a single-species stochastic modified Beverton–Holt model with Allee effects caused by predator saturation. We prove that, under some conditions on the parameters, there exists a Markov operator that is asymptotically stable. A stochastic version of the Cushing–Henson conjecture on attenuance and resonance is investigated.

Keywords:

• Allee effect
• stochastic
• attenuance
• resonance
• Markov operator
• asymptotic stability

AMS Subject Classifications:

• 39A11
• 92D25

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by a grant from King Abdul Aziz University, Saudi Arabia.