  Chaos synchronization in a ring of diffusively coupled nonlinear oscillators
driven by an external identical oscillator is studied. Based on numerical
simulations we show that by introducing additional couplings at $(mN_c+1)$-th
oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum
number of synchronized oscillators in the ring with a single coupling, the
maximum number of oscillators that can be synchronized can be increased
considerably beyond the limit restricted by size instability. We also
demonstrate that there exists an exponential relation between the number of
oscillators that can support stable synchronization in the ring with the
external drive and the critical coupling strength $\epsilon_c$ with a scaling
exponent $\gamma$. The critical coupling strength is calculated by numerically
estimating the synchronization error and is also confirmed from the conditional
Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling
relation exists for $m$ couplings between the drive and the ring. Further, we
have examined the robustness of the synchronous states against Gaussian white
noise and found that the synchronization error exhibits a power-law decay as a
function of the noise intensity indicating the existence of both noise-enhanced
and noise-induced synchronizations depending on the value of the coupling
strength $\epsilon$. In addition, we have found that $\epsilon_c$ shows an
exponential decay as a function of the number of additional couplings. These
results are demonstrated using the paradigmatic models of R\"ossler and Lorenz
oscillators.
