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In this paper we study a periodic impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Under general conditions, existence and uniqueness of solutions of such systems are established using ergodicity, Green functions and Gronwall integral inequality. Some sufficient conditions for the existence and stability of periodic solutions are shown and a new stability criterion based on linear approximation is proposed. Examples with constant and non-constant coefficients are simulated, illustrating the effectiveness of the results.