Phase Transitions in Active Rotator Systems

Abstract

In order to study the statistical dynamics of a large population of limit cycle oscillators or excitable elements, an active rotator model is introduced. This is defined dynamically as a stochastic version of a relaxational plannar model (with external field or anisotropy) modified by an additional constant driving force. Its numerical study based on a mean field treatment revealed the existence of a peculiar ordered phase in which individual motions are organized into a macroscopic rhythm. Two possible types of Transition to this ordered phase are also found.