Brusselator model

The Brusselator model is a theoretical model for a type of autocatalytic reaction that is capable of forming patterns. The best known real world examples is the Belousov-Zhabotinsky reaction. In this model we show how local and global parameters can be mixed in a model definition, and how special events can be set to happen at a certain time point. Explore how these work in the Events tab in the GUI. It consists of six species \(X\), \(Y\), \(A\) \(B\), \(D\) and \(E\). \(k_{i}\) are reaction parameters.

Formulation

\[ \begin{align}\begin{aligned}&\frac{\partial A}{\partial t} = D_{A} \nabla^2 A - A k_{1}\\&\frac{\partial B}{\partial t} = D_{B} \nabla^2 B - B X k_{3}\\&\frac{\partial X}{\partial t} = D_{X} \nabla^2 X + A k_{1} - B X k_{3} + X^{2} Y k_{2} - X k_{1}\\&\frac{\partial Y}{\partial t} = D_{Y} \nabla^2 Y + B X k_{3} - X^{2} Y k_{2}\\&\frac{\partial D}{\partial t} = D_{D} \nabla^2 D + B X k_{3}\\&\frac{\partial E}{\partial t} = D_{E} \nabla^2 E + X k_{1}\end{aligned}\end{align} \]

Example Snapshot

screenshot of the final step of the Brusselator example model — The final step of a run of the Brusselator model in SME.