The paper studies a Beverton-Holt difference equation, in which both the recruitment function and the survival rate vary randomly. It is then shown that there is a unique invariant density, which is asymptotically stable. Moreover, a basic theory for random mean almost periodic sequence on Z+ is given. Then, some suffcient conditions for the existence of a mean almost periodic solution to the stochastic Beverton-Holt equation are given.
Taylor & Francis
Bezandry, P.H., Diagana, T., & Elaydi, S. (2008). On the stochastic Beverton-Holt equation with survival rates. Journal of Difference Equations and Applications, 14(2), 175-190. doi:10.1080/10236190701565610
Journal of Difference Equations and Applications