Phase-locking phenomena in ergodically coupled CA phase oscillators and its theoretical analysis

Abstract

In this paper, phase-locking phenomena in two coupled cellular automaton (CA) phase oscillators for applying to central pattern generators (CPGs) are theoretically analyzed. The two CA phase oscillators are asynchronously coupled and referred to as the ergodically coupled CA phase oscillators since transition moments of discrete states are described by an irrational rotation. The theoretical analysis reveals stable fixed points that guarantee phase-locking in the ergodically coupled CA phase oscillators. It is then shown that the ergodically coupled CA phase oscillators are more suitable for applying to CPGs than the synchronously coupled CA phase oscillators in terms of phase-locking phenomena.