Bacterial Quorum Sensing — Bistable Switch
Autoinducer (AI) molecules accumulate with cell density. Above threshold, positive feedback drives collective gene activation. The bistable switch shows hysteresis: two stable states coexist over a range of densities, enabling collective decision-making.
Model: dA/dt = αρ·Aⁿ/(Kⁿ+Aⁿ) + αρ·ε - δA. The Hill function with cooperativity n≥2 creates positive feedback. Nullcline intersections give fixed points: stable (low AI) and stable (high AI) separated by an unstable saddle — the classic bistable switch. The saddle-node bifurcation points as ρ varies define the switching thresholds and hysteresis window.