On the steady states of weakly reversible chemical reaction networks
  A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the associated mass-action system. Furthermore, an index formula is given for the set of equilibria in a given stoichiometric compatibility class. 
Jian Deng, Christopher Jones, Martin Feinberg, Adrian Nachman
q-bio.QM physics.chem-ph