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PRODUCT-FORM POISSON-LIKE DISTRIBUTIONS AND COMPLEX BALANCED REACTION SYSTEMS.
- Source :
-
SIAM Journal on Applied Mathematics . 2016, Vol. 76 Issue 1, p411-432. 22p. - Publication Year :
- 2016
-
Abstract
- Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on Nn. Here we provide a fundamental characterization that connects structural properties of a network to its dynamical features. Specifically, we define the notion of "stochastically complex balanced systems" in terms of the network's stationary distribution and provide a characterization of stochastically complex balanced systems, parallel to that established in the 1970s and 1980s for deterministic reaction networks. Additionally, we establish that a network is stochastically complex balanced if and only if an associated deterministic network is complex balanced (in the deterministic sense), thereby proving a strong link between the theory of stochastic and deterministic networks. Further, we prove a stochastic version of the "deficiency zero theorem" and show that any (not only complex balanced) deficiency zero reaction network has a product-form Poisson-like stationary distribution on all irreducible components. Finally, we provide sufficient conditions for when a product-form Poisson-like distribution on a single (or all) component(s) implies the network is complex balanced, and we explore the possibility to characterize complex balanced systems in terms of product-form Poisson-like stationary distributions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361399
- Volume :
- 76
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 113584858
- Full Text :
- https://doi.org/10.1137/15M1029916