Synchronization Engineering: Theoretical Framework and Application to Dynamical Clustering

TL;DR

This paper introduces a phase model-based framework for designing nonlinear delayed feedback to control synchronization patterns in rhythmic populations, demonstrated through simulations and electrochemical experiments.

Contribution

It presents a novel theoretical framework for synchronization engineering using nonlinear delayed feedback, validated by numerical and experimental results.

Findings

Polynomial delayed feedback effectively tunes synchronization patterns

Engineered states include 1 to 4 clusters in electrochemical systems

Framework offers a versatile tool for controlling rhythmic populations

Abstract

A method for engineering the behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.