On the steady states of weakly reversible chemical reaction networks

Stochastically modeled weakly reversible reaction networks with a single linkage class

It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so long as the initial condition has strictly positive components). It is conjectured that the stochastically modeled analogs of these systems are positive recurrent. We prove this conjecture in the affirmative under the following additional assumptions: (i) the system is binary and (ii) for each species, there is a complex (vertex in the associated reaction dia…