Nonlinear Systems & Linearization · Challenge problem

The Brusselator chemical model with parameter $a = 4$ is $x' = 1 - (b + 1)x + 4x^2y,\; y' = bx - 4x^2y$ with $b > 0$. It has a single equilibrium, which loses stability (a Hopf bifurcation) at a critical value of $b$. Find that value.