Saturating autocatalytic switch

Forthe zero-input stable states are $0$ and $(k+\sqrt{k^2-4})/2$. The switching threshold is the saddle-node bifurcation determined by $f(g_c,s_c)={\partial }_{g}f(g_c,s_c)=0$ on the low-concentration branch.

For $k\gg 1$, the low-concentration saddle node of the saturating autocatalytic switch has