= Quadratic activator-inhibitor model
{title2=$u_t=u_{xx}+u^2/v-bu,\quad v_t=dv_{xx}+u^2-v$}
For positive concentrations and positive parameters, this <reaction–diffusion system> has homogeneous equilibrium $(u_*,v_*)=(1/b,1/b^2)$ and reaction <Jacobian matrix> $\begin{pmatrix}b&-b^2\\2/b&-1\end{pmatrix}$. Its trace is $b-1$ and determinant is $b$, making the equilibrium reaction-stable exactly when $0<b<1$. Stable complex eigenvalues permit damped oscillations, which must be distinguished from sustained periodic oscillations.
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