Synchronization stability in coupled oscillator arrays: Solution for arbitrary configurations

The stability of the state of motion in which a collection of coupled oscil lators are in identical synchrony is often a primary and crucial issue. Whe n synchronization stability is needed for many different configurations of the oscillators the problem can become computationally intense. In addition , there is often no general guidance on how to change a configuration to en hance or diminsh stability, depending on the requirements. We have recently introduced a concept called the Master Stability Function that is designed to accomplish two goals: (1) decrease the numerical load in calculating sy nchronization stability and (2) provide guidance in designing coupling conf igurations that conform to the stability required. In doing this, we develo p a very general formulation of the identical synchronization problem, show that asymptotic results can be derived for very general cases, and demonst rate that simple oscillator configurations can probe the Master Stability F unction.