  We consider the synchronization of solutions to coupled systems of the
conjugate random ordinary differential equations (RODEs) for the
$N$-Stratronovich stochastic ordinary differential equations (SODEs) with
linear multiplicative noise ($N\in \mathbb{N}$). We consider the
synchronization between two solutions and among different components of
solutions under one-sided dissipative Lipschitz conditions. We first show that
the random dynamical system generated by the solution of the coupled RODEs has
a singleton sets random attractor which implies the synchronization of any two
solutions. Moreover, the singleton sets random attractor determines a
stationary stochastic solution of the equivalently coupled SODEs. Then we show
that any solution of the RODEs converge to a solution of the averaged RODE
within any finite time interval as the coupled coefficient tends to infinity.
Our results generalize the work of two Stratronovich SODEs in \cite{9}.
