From Turing patterns to chimera states in the 2D Brusselator model

TL;DR

This paper explores how nonlocal coupling in the 2D Brusselator model leads to a transition from classical Turing patterns to chimera states, revealing new dynamical behaviors in reaction-diffusion systems.

Contribution

It demonstrates how tuning parameters in coupled Brusselators can induce a transition from Turing patterns to chimera states in two dimensions.

Findings

Classical Turing patterns are recovered in the diffusive limit.

Intermediate coupling ranges produce chimera states.

Parameters can be tuned to switch between stable patterns and chimera states.

Abstract

The Brusselator has been used as a prototype model for autocatalytic reactions, and in particular for the Belouzov- Zhabotinsky reaction. When coupled at the diffusive limit, the Brusselator undergoes a Turing bifurcation resulting in the formation of classical Turing patterns, such as spots, stripes and spirals in 2 spatial dimensions. In the present study we use generic nonlocally coupled Brusselators and show that in the limit of the coupling range R->1 (diffusive limit), the classical Turing patterns are recovered, while for intermediate coupling ranges and appropriate parameter values chimera states are produced. This study demonstrates how the parameters of a typical nonlinear oscillator can be tuned so that the coupled system passes from spatially stable Turing structures to dynamical spatiotemporal chimera states.