Nonlinear Systems & Linearization · Superchallenge problem

The Lorenz-type system $x' = 4(y - x),\; y' = rx - y - xz,\; z' = xy - z$ has, for $r > 1$, the equilibrium $C = \left(\sqrt{r - 1}, \sqrt{r - 1}, r - 1\right)$. As $r$ increases, $C$ loses stability when a pair of eigenvalues of its Jacobian crosses the imaginary axis. Find that value of $r$.