Tier structure of strongly endotactic reaction networks

David F. Anderson, Daniele Cappelletti, Jinsu Kim and Tung D. Nguyen

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7218-7259

Abstract: Reaction networks are mainly used to model the time-evolution of molecules of interacting chemical species. Stochastic models are typically used when the counts of the molecules are low, whereas deterministic models are often used when the counts are in high abundance. The mathematical study of reaction networks has increased dramatically over the last two decades as these models are now routinely used to investigate cellular behavior. In 2011, the notion of “tiers” was introduced to study the long time behavior of deterministically modeled reaction networks that are weakly reversible and have a single linkage class. This “tier” based argument was analytical in nature. Later, in 2014, the notion of a strongly endotactic network was introduced in order to generalize the previous results from weakly reversible networks with a single linkage class to this wider family of networks. The point of view of this later work was more geometric and algebraic in nature. The notion of strongly endotactic networks was later used in 2018 to prove a large deviation principle for a class of stochastically modeled reaction networks.

Keywords: Reaction networks; Continuous-time Markov chains; Stationary distribution; Large deviation principle; Ordinary differential equations; Lyapunov functions (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2020.07.012

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