dA/dt Nullcline (bistability)
State: —
Quorum sensing allows bacteria to count their population by secreting and
detecting a small signaling molecule (autoinducer, AI). A positive feedback loop with Hill-function
cooperativity creates bistability: at low cell density N, only the low-AI state is stable;
above a critical density, the system switches to the high-AI activated state, triggering collective
behaviors (bioluminescence, biofilm formation, virulence). The model: dA/dt = α·N·A²/(K²+A²) + β·N − δ·A
exhibits a saddle-node bifurcation as N increases.