A. V. Gasnikov, E. V. Gasnikova, “On Entropy-Type Functionals Arising in Stochastic Chemical Kinetics Related to the Concentration of the Invariant Measure and Playing the Role of Lyapunov Functions in the Dynamics of Quasiaverages”, Mat. Zametki, 94:6 (2013), 819–827; Math. Notes, 94:6 (2013), 854

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Matematicheskie Zametki, 2013, Volume 94, Issue 6, Pages 819–827
DOI: https://doi.org/10.4213/mzm10120 (Mi mzm10120)

This article is cited in 15 scientific papers (total in 15 papers)

On Entropy-Type Functionals Arising in Stochastic Chemical Kinetics Related to the Concentration of the Invariant Measure and Playing the Role of Lyapunov Functions in the Dynamics of Quasiaverages

A. V. Gasnikov, E. V. Gasnikova

Moscow Institute of Physics and Technology

Full-text PDF (501 kB) Citations (15)

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DOI: https://doi.org/10.4213/mzm10120

Abstract: This paper studies the relationship between the Lyapunov function of a macrosystem whose dynamics is governed by the laws of stochastic chemical kinetics and the invariant measure of this macrosystem arising at large times. A necessary and sufficient condition for the reduction of the search problem for the equilibrium of the macrosystem (the most probable macrostate of the invariant measure of this macrosystem) to an entropy-linear programming problem is given.

Keywords: entropy-type functional, stochastic chemical kinetics, Lyapunov function, dynamics of quasiaverages, equilibrium search problem, invariant measure, predator-prey model, Lotka–Volterra system.

Received: 03.08.2012
Revised: 21.02.2013

English version:
Mathematical Notes, 2013, Volume 94, Issue 6, Pages 854–861
DOI: https://doi.org/10.1134/S0001434613110229

Bibliographic databases:

Document Type: Article

UDC: 519.2

Language: Russian

Citation: A. V. Gasnikov, E. V. Gasnikova, “On Entropy-Type Functionals Arising in Stochastic Chemical Kinetics Related to the Concentration of the Invariant Measure and Playing the Role of Lyapunov Functions in the Dynamics of Quasiaverages”, Mat. Zametki, 94:6 (2013), 819–827; Math. Notes, 94:6 (2013), 854–861

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm10120

https://doi.org/10.4213/mzm10120

https://www.mathnet.ru/eng/mzm/v94/i6/p819

This publication is cited in the following 15 articles:

Evgenia Gasnikova, Alexander Gasnikov, Yaroslav Kholodov, Anastasiya Zukhba, “An Evolutionary View on Equilibrium Models of Transport Flows”, Mathematics, 11:4 (2023), 858
A. S. Ivanova, S. S. Omelchenko, E. V. Kotlyarova, V. V. Matyukhin, “Kalibrovka parametrov modeli rascheta matritsy korrespondentsii dlya g. Moskvy”, Kompyuternye issledovaniya i modelirovanie, 12:5 (2020), 961–978
D. R. Baymurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechenskii, E. I. Ershov, M. B. Kubentayeva, A. A. Lagunovskaya, “Universal method of searching for equilibria and stochastic equilibria in transportation networks”, Comput. Math. Math. Phys., 59:1 (2019), 19–33
Sergey Adzhiev, Janina Batishcheva, Igor Melikhov, Victor Vedenyapin, “Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem”, Physics, 1:2 (2019), 229
A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Num. Anal. Appl., 11:1 (2018), 16–32
S. Z. Adzhiev, V. V. Vedenyapin, S. S. Filippov, “$H$-theorem for continuous- and discrete-time chemical kinetic systems and a system of nucleosynthesis equations”, Comput. Math. Math. Phys., 58:9 (2018), 1462–1476
A. Gasnikov, E. Gasnikova, P. Dvurechensky, A. Mohammed, E. Chernousova, “About the power law of the PageRank vector distribution. Part 1. Numerical methods for finding the PageRank vector”, Num. Anal. Appl., 10:4 (2017), 299–312
S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “The $H$-theorem for the physico-chemical kinetic equations with explicit time discretization”, Physica A, 481 (2017), 60–69
S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “The $H$-theorem for the physico-chemical kinetic equations with discrete time and for their generalizations”, Physica A, 480 (2017), 39–50
S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “The $H$-theorem for the chemical kinetic equations with discrete time and for their generalizations”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012001
A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, A. V. Chernov, “Efficient numerical methods for entropy-linear programming problems”, Comput. Math. Math. Phys., 56:4 (2016), 514–524
A. V. Gasnikov, D. Yu. Dmitriev, “On efficient randomized algorithms for finding the PageRank vector”, Comput. Math. Math. Phys., 55:3 (2015), 349–365
A. V. Gasnikov, “Ob effektivnoi vychislimosti konkurentnykh ravnovesii v transportno-ekonomicheskikh modelyakh”, Matem. modelirovanie, 27:12 (2015), 121–136
A. V. Gasnikov, Yu. V. Dorn, Yu. E. Nesterov, S. V. Shpirko, “O trekhstadiinoi versii modeli statsionarnoi dinamiki transportnykh potokov”, Matem. modelirovanie, 26:6 (2014), 34–70
V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Russian Math. Surveys, 69:6 (2014), 995–1029

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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