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We consider a nonlinear discrete-time population model for the dynamics of an age-structured species. This model has the form of a Lure feedback system (well-known in control theory) and is a particular case of the system studied by Townley et al. in Townley et al. (2012). The main objective is to show that, in this case, the range of nonlinearities for which the existence of globally asymptotically stable non-zero equilibrium can be guaranteed is considerably larger than that in the main result in Townley et al. (2012). We illustrate our results with several biologically meaningful examples.