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Absract. In this study, we investigated the global asymptotic behaviors of their solutions by taking the second-order difference equation system. According to the given conditions, we obtained some asymptotic results for the positive balance of the system. We have also worked on q-fast changing functions. Such functions form the class of q-Caramate functions. We have applied q-Caramate functions to linear q-difference equations and We have also learned about the asymptotic behavior ofdoi:10.1051/itmconf/20182201050 fatcat:gazsefh7tjektl3ivqjqwfcsne