Self-amplifying reactions: A + B → 2B, exploring exponential growth, sigmoidal kinetics, and the origin of complexity
Autocatalysis: a product catalyzes its own formation.
A + B → 2B (rate = k₁[A][B])
Key features:
• Sigmoidal kinetics (slow→fast→slow)
• Exponential growth phase when [B]≪[A]
• Product limited by [A]_total
• Potential route to biological self-replication
"Cubic" autocatalysis: A → B at rate k₁[A][B]² — even sharper threshold, relevant to Turing patterns and the origin of life debates.