Design and control of noise-induced synchronization patterns

TL;DR

This paper introduces a method to control synchronization patterns in limit-cycle oscillators using common noisy inputs, leveraging linear filters and phase response properties, validated through numerical simulations.

Contribution

It presents a novel approach to induce and control various synchronization patterns in oscillators via noise filtering based on phase response analysis.

Findings

Effective control of synchronization patterns demonstrated

Optimal linear filters derived from phase response and noise spectrum

Numerical simulations confirm method validity

Abstract

We propose a method for controlling synchronization patterns of limit-cycle oscillators by common noisy inputs, i.e., by utilizing noise-induced synchronization. Various synchronization patterns, including fully synchronized and clustered states, can be realized by using linear filters that generate appropriate common noisy signals from given noise. The optimal linear filter can be determined from the linear phase response property of the oscillators and the power spectrum of the given noise. The validity of the proposed method is confirmed by numerical simulations.