Design principle of multi-cluster and desynchronized states in oscillatory media via nonlinear global feedback

TL;DR

This paper develops a theoretical framework for controlling spatial patterns in oscillatory media using nonlinear global feedback, enabling precise design of cluster and desynchronized states with potential experimental applications.

Contribution

It introduces a method to analytically determine feedback functions for specific spatial patterns in oscillatory media, including multi-cluster and desynchronized states.

Findings

Analytical feedback functions for 2-cluster, multi-cluster, and desynchronized states.

Numerical demonstration using the Brusselator model.

Discussion on potential experimental realization.

Abstract

A theoretical framework is developed for a precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the analysis of a phase diffusion equation with global coupling. In particular, feedback functions that generate the following spatial patterns are analytically given: i) 2-cluster states with an arbitrary population ratio, ii) equally populated multi-cluster states, and iii) a desynchronized state. Our method is demonstrated numerically by using the Brusselator model in the oscillatory regime. Experimental realization is also discussed.