ON MEASURES OF DISORDER IN GLOBALLY COUPLED OSCILLATORS

The transition from ordered to disordered behavior in an array of glob ally coupled phase oscillators is studied here using methods previousl y applied to the study of fluid turbulence. We apply a biorthogonal de composition of the ''space''-time data signal resulting from a finite sized array of oscillators under increasing disorder. Application of t hese methods requires identifying and measuring a useful signal that c aptures the dynamics of interest. We find that our method is very sens itive to changes in the system as a function of the disorder and ident ifies when an oscillator loses entrainment with the population. We stu dy finite sized systems and simultaneously compare our results to more traditional order parameters, the latter based on infinite sized syst ems. Copyright (C) 1998 Elsevier Science B.V.