Autocatalytic Reaction

A + B → 2B: autocatalysis, sigmoid growth, and connection to logistic equation

The autocatalytic reaction A + B → 2B follows d[B]/dt = k[A][B] = k([A₀]+[B₀]−[B])[B]. This is identical to the logistic equation with r = k·N_tot and K = N_tot: d[B]/dt = k·N_tot·[B](1−[B]/N_tot). The sigmoid S-curve reflects slow initial growth (limited B), explosive exponential growth, and saturation as A depletes. Autocatalysis underlies prion replication, crystallization, and origin-of-life scenarios.