Order Function and Macroscopic Mutual Entrainment in Uniformly Coupled Limit-Cycle Oscillators

Abstract

A concept of order function is proposed to develop a general self-consistent theory of mutual entrainment in large populations of limit-cycle oscillators such that each element is uniformly coupled to every other. The onset of entrainment is revealed to be a bifurcation of the order function in functional space. Numerical evidence for the theory is also presented.