  We study the effect of parameter fluctuations on synchronization of a coupled
chaotic system. The fluctuations to the parameter can be random or it can be a
periodic modulation. For random fluctuations we introduce a new quantity, the
\emph{rate of fluctuations}, apart from the statistical features of the
fluctuations. Fluctuation rate in our study refers to the number of random
modifications to parameters occurring in unit time. With a periodic modulation,
the fluctuation rates can be the frequency of the modulating term. It is found
that with high fluctuation rates the synchronization is stable irrespective of
the statistical or mathematical features of fluctuation. It was also found that
the low fluctuation rates can destroy synchronization even with a small
amplitude. We analytically explain the observed phenomenon using the dynamical
equations and numerically verified with a coupled system of Rossler attractor
as an example. We also numerically quantify the relation between
synchronization error and fluctuation rates.
