Chemical Reaction Network — Deficiency Zero Theorem

Feinberg 1972 · Detailed balance · Unique stable steady state

Network Selector

Species (n):
Complexes (c):
Linkage classes (l):
Deficiency δ = c−l−n:
Unique SS:
Deficiency Zero Theorem (Feinberg):
For a weakly reversible CRN with δ=0, the mass-action ODE system has exactly one positive steady state per stoichiometric class, and it is asymptotically stable.

δ = c − l − n
c = complexes, l = linkage classes, n = species

Brusselator has δ=2 — can oscillate (Hopf bifurcation). Schlögl has bistability.