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We present three examples of chemical reaction networks whose ordinarydifferential equation scaling limit are almost identical and in all casesstable. Nevertheless, the Markov jump processes associated to these reactionnetworks display the full range of behaviors: one is stable (positiverecurrent), one is unstable (transient) and one is marginally stable (nullrecurrent). We study these differences and characterize the invariant measuresby Lyapunov function techniques. In particular, we design a natural set of suchfunctions which scale homogeneously to infinity, taking advantage of the samescaling behavior of the reaction rates.

Seemingly stable chemical kinetics can be stable, marginally stable, or unstable