New conditions for pattern solutions of a Brusselator model

This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not. We introduce a new method to compute the degree index of the related linear operator so that the obtained sufficient conditions are easier to verify than those in the known references. The proofs mainly rely on Leray-Schauder degree theory, implicit function theorem and analytical techniques.