  We study the synchronization in a one dimensional array of point Josephson
junctions coupled to a common capacitor, which establishes a long-range
interaction between junctions and synchronizes them. The stability diagram of
synchronization in a noise-free system is obtained. The current when junctions
transform from resistive state into superconducting state, is then calculated
and its dependence on the shunt parameters and the dissipation of junctions is
revealed. In the presence of thermal noise, the synchronized oscillations are
destroyed at a critical temperature and the system undergoes a continuous phase
transition of desynchronization. A possible stability diagram of the
synchronized oscillations with respect to thermal noise, current, dissipations
and shunt capacitance is then constructed. Finally we investigate the dynamic
relaxation from random oscillations into synchronized state. The relaxation
time increases with the system size and temperature, but is reduced by the
shunt capacitor.
