Reaction Network Stoichiometry — Deficiency Zero Theorem

Mass-action kinetics, complex balancing, and when networks must have a unique steady state

Network—
Deficiency δ—
Species count—
Steady state—

Feinberg Deficiency Zero Theorem

For a mass-action network with deficiency δ = n − ℓ − s (complexes − linkage classes − stoichiometric subspace dim):

δ=0, weakly reversible → exactly one positive steady state per stoichiometric compatibility class; that steady state is globally stable.

Michaelis-Menten: δ=0, unique SS (no oscillations possible). Brusselator: δ=1, Hopf bifurcation possible → limit cycles. The network structure, not just kinetics, constrains dynamics.