Stochastic Robust Simulation and Stability Properties of Chemical Reaction Networks

In this paper, a novel algorithm to perform robust stochastic simulations of chemical reaction networks is proposed. Such a procedure relies on the definition of a stochastic difference inclusion, whose trajectories match those of the chemical reaction network. By taking advantage of the correspondence between chemical reaction networks and stochastic difference inclusions, mathematical tools available for the latter discrete-time systems are used to characterize stability properties of chemical reaction networks. Namely, Lyapunov conditions are given to guarantee asymptotic stability in probability, global strong recurrence, and global weak reachability of a given set for the reaction network. Practical examples of the application of the given algorithm and of the Lyapunov approach are reported.