A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability

Abstract

We develop a reduction method for general closed multiple time scale stochastic reaction networks for which the fast subsystem may have non-unique equilibrium probability. We obtain a reduced ODE system with nonhomogeneous terms whose solutions can approximate the solutions of the full system accurately. We then apply this reduction method to general linear network and nonlinear networks for which the state diagram can be constructed. We illustrate the accuracy of the reduction method by comparing computational results of the full systems with the reduced ODE systems for several examples. Finally, we show how the reduction method may be extended to three or more time scale reaction networks.