Turing instability and attractor bifurcation for the general Brusselator model

Abstract

In this paper, we analyze the dynamic bifurcation of the general Brusselator model when the order of reaction is p ∈ (1, ∞). We verify that the Turing instability occurs above the critical control number and obtain a rigorous formula for the bifurcated stable patterns. We define a constant sN that gives a criterion for the continuous transition. We obtain continuous transitions for sN > 0, but jump transitions for sN < 0. By using this criterion, we prove mathematically that higher-molecular reactions are rarely observed. We also provide some numerical results that illustrate the main results. © 2024 American Institute of Mathematical Sciences. All rights reserved.