The variation mechanism of the blazar is still an open question. In this study, we collect the long-term multi-wavelength data of 3C 454.3 to conduct a comprehensive study. The local cross-correlation functions were computed between the \(\gamma\) -ray and R band fluxes, as well as between B and K band fluxes. No significant time lags were found among these bands, which suggests that the optical and \(\gamma\) -ray emissions are co-spatial. The color indices variation behavior showed a redder-when-brighter trend in the lower state, and a saturation state in the higher state. The slope of the linear correlations between the logarithms of synchrotron and inverse-Compton fluxes changed from 0.61 to 3.34 for different band pairs, which could be explained by a model of Doppler-boosted log-parabolic synchrotron emission combined with stable background contamination. The model could also reproduce the spectral energy distributions at different brightness. This study can help us to better understand the variation mechanism of blazars.
