  This work is about the synchronization of nonlinear coupled dynamical systems
driven by $\alpha$-stable noise. Firstly, we provide a novel technique to
construct the relationship between synchronized system and slow-fast system.
Secondly, we show that the slow component of original systems converges to the
mild solution of the averaging equation under $L^{p}(1<p<\alpha)$ sense.
Finally, using the results of averaging principle for stochastic dynamical
system with two-time scales, we show that the synchronization effect is
persisted provided equilibria are replaced by stationary random solutions.
