Bulk stability of bimolecular stochastic chemical reaction networks
Andrea Agazzi, Lucie Laurence
Source abstract
We establish criteria for stability in the bulk of planar stochastic chemical reaction networks with mass-action kinetics. Using Poincaré 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.
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