Solutions of the Brusselator Model

Its stability is studied by slightly changing the stationary concentrations by small quantities x and y  

After algebraic transformations and n lecting second-order (and third-order) terms that imply crossed concentrations such as xx, yy or xy, one obtains  

Its non-trivial solutions (x 0 et y 0) are obtained as the roots of the secular determinant  

The Brasselator solutions have five specific behaviors according to the respective values of the concentrations of A and B  

The oscillatory behaviors are obtained when the value of the discriminant is negative  

---