SELF-SYNCHRONIZATION OF MANY COUPLED OSCILLATORS

We investigate the synchronization to a common frequency and phase in systems of many coupled digital phase-locked loops. We study cases for which the internal frequencies are identical for all loops and for which they are different. In both cases, we observe that synchronization to a common frequency is possible in a range of the parameter space. We find an analytical expression for the synchronization frequency when the communication between loops is in two directions. Synchronization in phase occurs only when the internal frequencies of the loops are identical. We study the transient convergence to the locked state in the ring, double ring, and global coupling configurations. We also discuss the in fluence of a multiperiodic or chaotic loop on the dynamics of the system. Our results may have applications to the problem of network synchronization.