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In this paper, the existence and global exponential stability of periodic solution is investigated for a class of impulsive bidirectional associative memories neural networks that possesses a Cohen-Grossberg dynamics incorporating variable delays and time-variant coefficients. By using compressive mapping and Lyapunov functional, sufficient conditions are obtained to guarantee the existence and uniqueness of the periodic solution and its global exponential stability. We can see that impulses contribute to the existence and stability of periodic solution for this system. Some comparisons and examples are given to demonstrate the effectiveness of the obtained results. The model studied in this paper is a generalization of some existing models in literature, including Hopfield neural networks, BAM neural networks with impulse and time delays, Cohen-Grossberg neural networks, and thus, the main results of this paper generalize some results in literature.