  We have developed a simple cellular automata model for nonlinearly coupled
phase oscillators which can exhibit many important collective dynamical states
found in other synchronizing systems. The state of our system is specified by a
set of integers chosen from a finite set and defined on a lattice with periodic
boundary conditions. The integers undergo coupled dynamics over discrete time
steps. Depending on the values of coupling strength and range of coupling, we
observed interesting collective dynamical phases namely: asynchronous, where
all the integers oscillate incoherently; synchronized, where all integers
oscillate coherently and also other states of intermediate and time-dependent
ordering. We have adapted conventional order parameters used in coupled
oscillator systems to measure the amount of synchrony in our system. We have
plotted phase diagrams of these order parameters in the plane of strength of
coupling and the radius of coupling. The phase diagrams reveal interesting
properties about the nature of the synchronizing transition. There are
partially ordered states, where there are synchronized clusters which are shown
to have a power law distribution of their sizes. The power law exponent is
found to be independent of the system parameters. We also discuss the
possibility of chimera states in this model. A criterion of persistence of
chimera is developed analytically and compared with numerical simulation.
