Noise-induced Synchronization in Small World Network of Phase Oscillators

TL;DR

This paper investigates how noise influences synchronization in small-world networks of phase oscillators, revealing that intermediate noise levels can enhance synchronization by eliminating defect patterns inherited from regular networks.

Contribution

It demonstrates the phenomenon of stochastic synchronization in small-world networks and links it to the suppression of defect patterns caused by noise.

Findings

Intermediate noise levels increase synchronization.

Defect patterns are suppressed by noise.

Stochastic synchronization observed in natural networks.

Abstract

A small-world network (SW) of similar phase oscillators, interacting according to the Kuramoto model is studied numerically. It is shown that deterministic Kuramoto dynamics on the SW networks has various stable stationary states. This can be attributed to the "defect patterns" in a SW network which is inherited to it from deformation of "helical patterns" in its parent regular one. Turning on an uncorrelated random force, causes the vanishing of the defect patterns, hence increasing the synchronization among oscillators for intermediate noise intensities. This phenomenon which is called "stochastic synchronization" generally observed in some natural networks like brain neuronal network.