Fig. 4

Bifurcation diagram for the non-spatial version of model (2.3)-(2.4) showing the steady state values of oxygen concentration \(\hat{c}\) as a function of the oxygen production rate. Other parameters are given in Table 1. For \(A<A_{\min }\approx 0.937\), there exists only the trivial ‘extinction’ solution, \((\hat{c},\hat{u})=(0,0)\) (red line), which is always stable. For \(A>A_{\min }\), there are also two positive steady states, one of the stable (solid green curve), the other unstable (dotted black curve).