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Mat. Zametki, 2013, Volume 94, Issue 6, Pages 819–827 (Mi mz10120)  

This article is cited in 11 scientific papers (total in 11 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

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.

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

Full text: PDF file (501 kB)
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English version:
Mathematical Notes, 2013, 94:6, 854–861

Bibliographic databases:

UDC: 519.2
Received: 03.08.2012
Revised: 21.02.2013

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

    This publication is cited in the following articles:
    1. 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  mathnet
    2. V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Russian Math. Surveys, 69:6 (2014), 995–1029  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. V. Gasnikov, D. Yu. Dmitriev, “On efficient randomized algorithms for finding the PageRank vector”, Comput. Math. Math. Phys., 55:3 (2015), 349–365  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. V. Gasnikov, “Ob effektivnoi vychislimosti konkurentnykh ravnovesii v transportno-ekonomicheskikh modelyakh”, Matem. modelirovanie, 27:12 (2015), 121–136  mathnet  elib
    5. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    6. 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  mathnet  crossref  crossref  isi  elib
    7. 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  crossref  mathscinet  isi
    8. 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  crossref  mathscinet  isi
    9. 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  crossref  isi
    10. 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  mathnet  crossref  crossref  isi  elib
    11. 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  mathnet  crossref  crossref  isi  elib
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