Parameter fluctuations in coupled chaotic systems
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.