Fig. 6

Zoom onto isocline intersections with varying parameters. a Varying growth rate difference, \(\delta \alpha _1 = 10^{-1}\dots 10^{-3}\), shifts the composition isocline (orange lines), but leaves the population size isocline (blue lines) almost unaffected: The fixed point is unstable as long as the intersection is on the antibiotics-limited part of the population isocline (red open circles), and becomes stable when the intersection moves to the resource-limited part (green filled circles). Intersections close to the transition have complex eigenvalues, which can be stable (purple filled circles) or unstable (purple open circles). The unstable fixed point can support a stable limit cycle (purple open circles), not contained in the linearized analysis. b Increasing the dilution rate shifts the population size isocline. Parameters in both panels are \(B_0/\mu =1.25\) and \(\rho _1/\alpha =5\cdot 10^{-3}\), \(\kappa =\gamma =2\)