Spatiotemporal fluctuation induces Turing pattern formation in the chemical Brusselator

Abstract

Chemical reactions are embedded in spatiotemporal fluctuations instead of a constant environment. Here, we aimed to assess reaction–diffusion (RD) with dichotomous noise-controlling system parameters in the Brusselator and examine the effect of these fluctuations on the dynamic behavior of chemical reactions. By performing a multiscale perturbation analysis, we demonstrated that the correlated noise can broaden the Turing region even if molecular memory (autocorrelation time) exists. However, for small noise, short-term memory promotes Turing instability. The instability of the Brusselator is determined by the noise strength, which belongs to the optimal region if the diffusion coefficient is fixed. Turing pattern selection and stability are also governed by the dynamic character of the amplitude equation, and the entire Turing instability region shifts to the right in the phase space with noise perturbation. Finally, numerical simulations validate the theoretical derivation that correlated noise can amplify Turing pattern formation to maintain distinct patterns.