Figure 4.

Increasing the QS signal feedback exponent α causes hysteretic response to population changes. Steady state QS signal concentration, S^* as function of the population size N, plotted for four different values of the QS feedback exponent α = [1.0, 1.2, 1.5, 2.0]. When $\alpha >{\alpha }_c=\frac{2+{\sigma }_s^{max}+2\sqrt{1+{\sigma }_s^{max}}}{{\sigma }_s^{max}}\approx 1.2210$ the system will be bistable for a certain range of population sizes. (${\sigma }_S^{max}=100$, concentration of S is here given in units of ${\sigma }_S^{basal}∕{\gamma }_S$. ${\sigma }_S^{basal}$ is the basal production rate and γ_S is the degradation/depletion rate of the of signal, which is here set to 1.)