Turing Instability Suppressed and Induced by Multiplicative Noise in Brusselator System

Abstract: The effect of multiplicative noise to the Turing instability of the Brusselator system is investigated. We show that when the noise acts on both of the concentrations with the same intensities, then the Turing instability is suppressed provided that the intensities are sufficiently large. This aligns with the stabilizing effect of multiplicative noise in partial differential equations. Utilizing the linearized system, we can quantify the magnitude of noise which stabilizes the system. On the other hand, when the noise is involving only one concentration, then the Turing instability can be triggered with suitable intensities. These are confirmed by numerical simulations.