Figure 3
From: Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect
Bifurcation analysis reveals regions of bistability. (A) heatmap showing the equilibrium density \(\rho \) of Eq. (5) as a function of the Allee parameter \(a\) and the dilution rate \(\,d\). The different regimes correspond to survival (I), bistability between survival and extinction (II), and extinction (III). (B) Influence of the dilution \(\,d\), for \(a=0.2\) kept constant. (C) Influence of the Allee parameter \(a\), for \(\,d=0.3\) kept constant. (D) Visual interpretation of the equilibrium states, corresponding to the intersection of the per capita growth rate and the dilution, showing how increasing the dilution shifts regime I into regime II, into regime III. (E) The Allee parameter \(a\) has the opposite effect than the dilution \(\,d\): increasing \(a\) allows for survival by shifting regime III into regime II into regime I. Parameter values: \({r}_{a}=1\), \({C}_{a}=1\).
