THE ROLE OF SYMMETRY-BREAKING AND DISORDER IN THE CONTROL OF PHASE-ORDERED STATES IN GLOBALLY COUPLED OSCILLATORS

We investigate the dynamics of splay-phase states, special out-of-phas e states, in an array of globally coupled phase oscillators. Using asy mptotic methods and a dimension reducing coordinate transformation we derive explicit representation for saddle shaped surfaces on which the dynamics is confined. The restricted motion is due to a high degree o f neutral stability possessed by the splay-phase and related incoheren t states. An additional consequence of the neutral stability is an ext reme sensitivity to intrinsic noise which leads to diffusive drift. Th e elimination of this drift motivates an examination of the effect of parameter perturbations and their use for control. We have found that the system is uncontrollable using symmetry-preserving perturbations, but that symmetry-breaking perturbations effectively allow for the pre vention of noise-induced drift. Finally, we have made observations on how general disorder affects the dynamics of the system; in particular , for small disorder certain sums of the phases become unbounded while others remain fixed.