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In this paper we study and obtain the existence of almost periodic solutions to the following class of semilinear difference equations whereA, Bare singularsquare matrices () andis almost periodic in the first variable uniformly in the second one. Next, we use these results to study the existence of almost periodic to some second-order (and higher-order) singular difference equations. [ABSTRACT FROM PUBLISHER]

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 [image omitted] is given. Then, some sufficient conditions for the existence of a mean almost periodic solution to the stochastic Beverton-Holt equation are given. [ABSTRACT FROM AUTHOR]

We establish the basic theory of almost periodic sequences on +. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models. [ABSTRACT FROM AUTHOR]