Synchronization Patterns in Geometrically Frustrated Turing Rings

TL;DR

This paper investigates synchronization patterns in rings of coupled nonlinear oscillators, specifically Brusselators, revealing discrepancies with traditional analysis and proposing a piecewise linear approximation for explanation.

Contribution

It introduces a novel piecewise linear approximation to explain complex synchronization behaviors in strongly nonlinear coupled oscillators.

Findings

Rings of coupled Brusselators do not follow classical turning analysis predictions.

A piecewise linear model successfully explains observed behaviors.

Strong nonlinearity leads to canard explosions in the system.

Abstract

Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that leads to a canard explosion in a single Brusselator. In this highly nonlinear regime it is numerically found that rings of coupled Brusselators do not follow the predictions from Turning analysis. We find that the behavior can be explained using a piecewise linear approximation.