Fig. 4.

The subcritical HB can be controlled by the time delay ($\tau$). (A) Bifurcation diagram as a function of $\tau$, for $C=1,\alpha =10,\beta =1,\gamma =1,\delta =10$. (B) Analytic relationship between the oscillation period and the time delay for different values of $\delta$ (solid lines), according to Eq. 17. The green dashed line shows the limit of infinite $\delta$: $T=2\tau$. (C) Numerical relationship between the oscillation period and the time delay for the same parameter values as in A. The light blue line is the result of continuation analysis with DDE-BIFTOOL, the blue solid circles show simulation results, and the green dashed line is the relationship $T=2\tau$, for reference and comparison with B. (D) Period at the oscillation onset as a function of biofilm size (radius). Scatterplot, experimental data; gray line, linear fit; r, correlation coefficient; p, P value.