Results on stochastic reaction networks with non-mass action kinetics

DOI10.3934/mbe.2019103zbMath1501.92223arXiv1712.01716OpenAlexW2963140410WikidataQ92346792 ScholiaQ92346792MaRDI QIDQ2091896

David F. Anderson, Tung D. Nguyen

Publication date: 2 November 2022

Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.01716

zbMATH Keywords

stationary distributioncontinuous-time Markov chainsreaction networksnon-mass action kineticsexplosivityLyapunnov functions

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Biochemistry, molecular biology (92C40) Systems biology, networks (92C42)

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Cites Work

• Product-form stationary distributions for deficiency zero networks with non-mass action kinetics
• Product-form stationary distributions for deficiency zero chemical reaction networks
• A new method for choosing the computational cell in stochastic reaction-diffusion systems
• Univalent positive polynomial maps and the equilibrium state of chemical networks of reversible binding reactions
• Lyapunov functions, stationary distributions, and non-equilibrium potential for reaction networks
• Representations of Markov processes as multiparameter time changes
• Strong approximation theorems for density dependent Markov chains
• Large deviations theory for Markov jump models of chemical reaction networks
• Non-explosivity of stochastically modeled reaction networks that are complex balanced
• Mathematical formalism of nonequilibrium thermodynamics for nonlinear chemical reaction systems with general rate law
• Product-Form Poisson-Like Distributions and Complex Balanced Reaction Systems
• Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction
• Stochastic Analysis of Biochemical Systems
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