Toggle switch: two genes A, B mutually repress each other via Hill functions. ẋ = α/(1+(y/K)ⁿ) − x. Deterministic system has two stable fixed points (A-ON, B-OFF and vice versa). Stochastic Gillespie simulation shows noise-induced transitions between states. Bimodal histogram reveals the probability of each state. Increase Hill coefficient n for sharper switching.