We present some existence and localization results for periodic
solutions of impulsive first-order coupled non-linear systems of two
equations, without requiring periodicity for the nonlinearities. The
arguments are based on Schauder's Fixed Point Theorem together with the
upper and lower solution method, where the upper and lower solutions are
not necessarily well-ordered. In addition, results on equi-regulated
functions are required for the impulsive analysis. An application to a
Wilson-Cowan system of two strongly coupled neurons illustrates one of
the main results.