The effects of noise and time delay on the synchronization of the Kuramoto model in small-world networks

TL;DR

This paper investigates how noise and time delay influence synchronization in small-world networks of Kuramoto oscillators, revealing multiple attractors, noise-enhanced synchronization, and phase transitions driven by delay variations.

Contribution

It introduces a comprehensive analysis of the combined effects of noise and time delay on Kuramoto model synchronization in small-world networks, including new phase transition insights.

Findings

Noise can enhance synchronization in the model.

Time delay induces multiple phase transitions between synchronized and incoherent states.

Average oscillator frequency decreases with increasing delay, with abrupt jumps at transition points.

Abstract

We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of each node. For this model, similar to the constant coupling studied before, we find the existence of various attractors corresponding to the different defect patterns and also the noise enhanced synchronization when driven by an external uncorrelated white noise. We also investigate the synchronization of the model with homogenous time-delay in the phase couplings. For a given intrinsic frequency and coupling constant, upon varying the time delay we observe the existence a partially synchronized state with defect patterns which transforms to an incoherent phase characterized by randomly phase locked states. By further increasing of the time delay, this phase again undergoes a transition to another patterned partially synchronized state. We show that the transition between theses phases are discontinuous and moreover in each phase the average frequency of the oscillators decreases by increasing the time delay and shows an upward jump at the transition points.