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In this paper, we study the stability of the zero equilibria of two close-to-symmetric systems of difference equations with exponential terms in the special case in which one of their eigenvalues is equal to −1 and the other eigenvalue has an absolute value of less than 1. In the present study, we use the approach of center manifold theory.doi:10.3390/sym10060188 fatcat:ltubplcrv5fnvhjds7wi4p3kga