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

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.