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Mat. Zametki, 2008, Volume 83, Issue 4, Pages 606–612 (Mi mz3778)  

This article is cited in 20 scientific papers (total in 20 papers)

$F$-Quadratic Stochastic Operators

U. A. Rozikova, U. U. Zhamilovb

a Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
b Lycee no. 43

Abstract: In this paper, we introduce the notion of an $F$‑quadratic stochastic operator. It is shown that each $F$-quadratic operator has a unique fixed point. Besides, it is proved that any trajectory of an $F$-quadratic stochastic operator exponentially rapidly converges to this fixed point.

Keywords: quadratic stochastic operator, non-Volterra stochastic operator, ergodic theorem, mathematical genetics, fixed point of an operator

DOI: https://doi.org/10.4213/mzm3778

Full text: PDF file (487 kB)
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English version:
Mathematical Notes, 2008, 83:4, 554–559

Bibliographic databases:

UDC: 519.2
Received: 28.02.2007
Revised: 10.04.2007

Citation: U. A. Rozikov, U. U. Zhamilov, “$F$-Quadratic Stochastic Operators”, Mat. Zametki, 83:4 (2008), 606–612; Math. Notes, 83:4 (2008), 554–559

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Rozikov U. A., Zada A., “On $l$-Volterra quadratic stochastic operators”, Dokl. Math., 79:1 (2009), 32–34  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. U. U. Zhamilov, U. A. Rozikov, “The dynamics of strictly non-Volterra quadratic stochastic operators on the 2-simplex”, Sb. Math., 200:9 (2009), 1339–1351  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Rozikov U.A., Zada A., “On dynamics of $\ell$-Volterra quadratic stochastic operators”, Int. J. Biomath., 3:2 (2010), 143–159  crossref  mathscinet  zmath  isi  elib  scopus
    4. Rozikov U.A. Zhamilov U.U., “Volterra quadratic stochastic operators of a two-sex population”, Ukr. Math. J., 63:7 (2011), 1136–1153  crossref  mathscinet  zmath  isi  scopus
    5. Ganikhodzhaev R. Mukhamedov F. Rozikov U., “Quadratic stochastic operators and processes: results and open problems”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 14:2 (2011), 279–335  crossref  mathscinet  zmath  isi  elib  scopus
    6. Rozikov U.A. Zada A., “$\ell$-Volterra quadratic stochastic operators: Lyapunov functions, trajectories”, Appl. Math. Inf. Sci., 6:2 (2012), 329–335  mathscinet  isi
    7. Ladra M., Rozikov U.A., “Evolution Algebra of a Bisexual Population”, J. Algebra, 378 (2013), 153–172  crossref  mathscinet  zmath  isi  elib  scopus
    8. Shahidi F.A., Abu Osman M.T., “The Limit Behaviour of Trajectories of Dissipative Quadratic Stochastic Operators on Finite-Dimensional Simplex”, J. Differ. Equ. Appl., 19:3 (2013), 357–371  crossref  mathscinet  zmath  isi  scopus
    9. Shahidi F., “On Infinite-Dimensional Dissipative Quadratic Stochastic Operators”, Adv. Differ. Equ., 2013, 272  crossref  mathscinet  zmath  isi  scopus
    10. Mukhamedov F. Saburov M. Qaralleh I., “On XI((S))-Quadratic Stochastic Operators on Two-Dimensional Simplex and their Behavior”, Abstract Appl. Anal., 2013, 942038  crossref  mathscinet  isi  scopus
    11. Blath J. Jamilov U.U. Scheutzow M., “(G, Mu)-Quadratic Stochastic Operators”, J. Differ. Equ. Appl., 20:8 (2014), 1258–1267  crossref  mathscinet  zmath  isi  scopus
    12. Ganikhodzhaev N.N. Zhamilov U.U. Mukhitdinov R.T., “Nonergodic Quadratic Operators For a Two-Sex Population”, Ukr. Math. J., 65:8 (2014), 1282–1291  crossref  mathscinet  zmath  isi  scopus
    13. Davronov R.R., Jamilov U.U., Ladra M., “Conditional Cubic Stochastic Operator”, J. Differ. Equ. Appl., 21:12 (2015), 1163–1170  crossref  mathscinet  zmath  isi  scopus
    14. Mukhitdinov R., “Constrained Quadratic Stochastic Operators”, TWMS J. Pure Appl. Math., 6:2 (2015), 233–237  mathscinet  zmath  isi
    15. Jamilov U.U. Ladra M., “F-evolution algebra”, Filomat, 30:10 (2016), 2637–2652  crossref  mathscinet  zmath  isi  elib  scopus
    16. Jamilov U.U. Scheutzow M. Wilke-Berenguer M., “On the random dynamics of Volterra quadratic operators”, Ergod. Theory Dyn. Syst., 37:1 (2017), 228–243  crossref  mathscinet  zmath  isi  elib  scopus
    17. Qaralleh I., “Classification of a New Subclass of Xi((a S)) - Qso and Its Dynamics”, J. Math. Comput. Sci.-JMCS, 17:4 (2017), 535–544  crossref  isi
    18. Jamilov U.U. Ladra M. Mukhitdinov R.T., “On the Equiprobable Strictly Non-Volterra Quadratic Stochastic Operators”, Qual. Theor. Dyn. Syst., 16:3 (2017), 645–655  crossref  mathscinet  zmath  isi  scopus
    19. Alsarayreh A. Qaralleh I. Ahmad M.Z., “Xi((as))-Quadratic Stochastic Operators in Two-Dimensional Simplex and Their Behavior”, JP J. Algebr. Number Theory Appl., 39:5 (2017), 737–770  crossref  isi  scopus
    20. Jamilov U.U. Khamraev A.Yu. Ladra M., “On a Volterra Cubic Stochastic Operator”, Bull. Math. Biol., 80:2 (2018), 319–334  crossref  mathscinet  zmath  isi  scopus
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