Biology & Math
Selkov (1968) modeled phosphofructokinase allosteric feedback. Product ADP activates its own production — positive feedback that creates a limit cycle.
ẋ = -x + a·y + x²y
ẏ = b - a·y - x²y
x = ADP concentration; y = ATP concentration. Oscillations require b² < a + (a/b)² roughly — a Hopf bifurcation boundary.