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.
Similar content being viewed by others
References
Gillespie D.T.: Physica A 188, 404–425 (1992)
C.H. Lee, R. Lui, J. Math. Chem., (2009 in press)
Gillespie D.T.: J. Phys. Chem. 81, 2340–2361 (1977)
Rao C.V., Arkin A.P.: J. Chem. Phys. 118, 4999–5010 (2003)
Cao Y., Gillespie D.T., Petzold L.R.: J. Chem. Phys. 122, 014116 (2005)
Peleš S., Munsky B., Khammash M.: J. Chem. Phys. 125, 204104 (2006)
Schuster S., Hilgetag C.: J. Phys. Chem. 99, 8017–8023 (1995)
Temkin O.N., Zeigarnik A.V., Bonchev D.: Chemical Reaction Networks: A Graph-Theoretical Approach. CRC Press, Boca Raton (1996)
Ch. Ottinger, Branching ratios in chemical reactions, Proceedings of the NATO Advanced Research Workshop on Selectivity in Chemical Reactions, Bowness-on-Windermere, U.K., 427–455 (1988) September (1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lee, C.H., Lui, R. A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability. J Math Chem 47, 750–770 (2010). https://doi.org/10.1007/s10910-009-9598-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-009-9598-1