Pseudo compact almost automorphic solutions for a family of delayed population model of Nicholson type

In this paper, we consider a generalized differential equation with feedback and time-varying delays and prove the existence of a unique pseudo compact almost automorphic solution that is exponentially attractive. We show our result by applying the Banach fixed point theorem and the properties of pseudo compact almost automorphic function. We apply our results and obtain new criteria for the existence and convergence dynamics of pseudo compact almost automorphic solutions for some models that involves sum of nonlinear terms that satisfy a general condition. These models are very general and include sums of unimodals terms with monotones, such as Nicholson, Mackey-Glass, Lasota-Wazeska and others. The results obtained are new and they recover, extend and improve recent works.