The Kuramoto model: A simple paradigm for synchronization phenomena

TLDR

Synchronization of large interacting populations is a major research focus across many fields, often approached by modeling each member as a phase oscillator. The review analyzes synchronization using the Kuramoto model, a representative coupled phase oscillator model. The review presents a rigorous mathematical treatment, numerical methods, recent variations and extensions of the Kuramoto model, and its applications across diverse contexts.

Abstract

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included.