Violent multi-wavelength variabilities are observed in gamma-ray-selected blazars. We present an analysis of long-term light curves for eight bright blazars to explore the co-variation pattern in the gamma-ray and radio bands. We extract their gamma-ray light curves and spectra with data observed by the Fermi/LAT since 2008. We find diverse co-variation patterns between the gamma-ray and radio (at 43 GHz) fluxes in these sources. The gamma-ray and radio fluxes of 3C 454.3 and PKS 1633+382 are correlated without any time-lag, suggesting that they are from the same radiation region. Similar correlation is also observed in 3C 273 and PKS 1222+216, but the radio flux is lag behind the gamma-ray flux approximately ~160 days and ~290 days, respectively. This likely suggests that their gamma-ray emission regions are located at the upstream of their radio cores at 43 GHz. The gamma-ray and radio fluxes of the other four blazars are not correlated, implying that the gamma-ray and radio emission may be from different regions in their jets. The gamma-ray light curves of the eight blazars can be decomposed into some long timescale variability components and fast spike flares. We propose that they may be attributed to the central engine activity and the magnetic reconnection process or turbulence in the local emission region, respectively.
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