We study the stability of chaos synchronization in the linearly coupled chaotic systems array. In particular, effects of a coupling strength to the overall system dynamics in diffusively coupled R$ö$ssler systems array are investigated. Lyapunov exponents for each coupling strength are calculated to determine the condition for synchronization, and compared with transverse variations and spatial amplitudes of possible modes. The expected short wavelength bifurcation is certified in χ-directionally coupled array, though that the Lyapunov exponent is insufficient to guarantee the stable synchronization near thresholds is also showed.
