Global qualitative dynamics of the Brusselator system

Dynamic transitions and Turing patterns of the Brusselator model

“…An autocatlytic reaction is one in which a species acts to increase the rate of its producing reaction. In many autocatlytic systems, multiple steady states and periodic orbits are usually seen 14 . The chemical reaction of the Brusselator model consists of four irreversible steps, given by $$$$ {\displaystyle \begin{array}{c}\overset{k_1}{A\to X}\\ {}\overset{k_2}{B+X\to Y+D}\\ {}2X+Y\overset{k_3}{\to }3X\\ {}\overset{k_4}{X\to E}\end{array}} $$$$ where $$$ X $$$ and $$$ Y $$$ are components which vary in time and space, $$$ A $$$ and $$$ B $$$ are constant components while $$$ D $$$ and $$$ E $$$ are products.…”

“…In many autocatlytic systems, multiple steady states and periodic orbits are usually seen. 14 The chemical reaction of the Brusselator model consists of four irreversible steps, given by…”