Bulk stability of bimolecular stochastic chemical reaction networks

Abstract

We establish criteria for stability in the bulk of planar stochastic chemical reaction networks with mass-action kinetics. Using Poincar\'e compactification, we characterize the asymptotic drift and show how stochastic fluctuations can prevent escape along transversally repulsive branches of the limiting deterministic flow. We construct a Lyapunov function by combining local estimates near these branches with dissipative estimates in the neighboring regions. The criteria cover a wide class of networks and in particular apply beyond weakly reversible and strongly endotactic networks. Together with compatible boundary estimates, these criteria imply positive recurrence.