In the paper, we deal with a reaction-diffusion system well known as the Brusselator model and some improved results for the steady states of this model are presented. We first give an a priori estimates (positive upper and lower bounds) of positive steady states. Then, we obtain the non-existence and existence of positive non-constant steady states as the parameters λ, θ and b are varied, which means some certain conditions under which the pattern formation occurs or not. © 2005 Elsevier Inc. All rights reserved.
Peng, R., & Wang, M. (2005). Pattern formation in the Brusselator system. Journal of Mathematical Analysis and Applications, 309(1), 151–166. https://doi.org/10.1016/j.jmaa.2004.12.026