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References (34)
-
(2011)
Results and open problems,” Infinite Dimens -
N. Ganikhodjaev, R. Ganikhodjaev, U. Jamilov (2014)
Quadratic stochastic operators and zero-sum game dynamicsErgodic Theory and Dynamical Systems, 35
-
U. Jamilov, A. Reinfelds (2020)
On constrained Volterra cubic stochastic operatorsJournal of Difference Equations and Applications, 26
-
R. Ganikhodzhaev, F. Mukhamedov, U. Rozikov (2011)
QUADRATIC STOCHASTIC OPERATORS AND PROCESSES: RESULTS AND OPEN PROBLEMSInfinite Dimensional Analysis, Quantum Probability and Related Topics, 14
-
A. Yu. Khamraev (2009)
On a Volterra type cubic operatorsUz.M.J., 3
-
R. Davronov, U. Jamilov, M. Ladra (2015)
Conditional cubic stochastic operatorJournal of Difference Equations and Applications, 21
-
H. Kesten (1970)
Quadratic transformations: a model for population growth. IAdvances in Applied Probability, 2
-
S. Bernstein (1942)
Solution of a Mathematical Problem Connected with the Theory of HeredityAnnals of Mathematical Statistics, 13
-
I︠u︡. Li︠u︡bich, E. Akin, D. Vulis, A. Karpov (1992)
Mathematical structures in population geneticsThe Mathematical Gazette, 78
-
(1960)
A Collection of Mathematical Problems, Vol. 8 of Interscience Tracts in Pure and Applied Mathematics (Interscience -
A. Yu. Khamraev (2004)
On cubic operators of Volterra typeUz.M.J., 2
-
U. Jamilov, M. Scheutzow, Isabell Vorkastner (2019)
A prey–predator model with three interacting speciesDynamical Systems, 38
-
U. Rozikov, A. Khamraev (2014)
On Construction and a Class of Non-Volterra Cubic Stochastic Operators -
R. Devaney (1990)
An Introduction to Chaotic Dynamical Systems -
M. Bernhard (1992)
Introduction to Chaotic Dynamical Systems -
F. Mukhamedov, C. Pah, A. Rosli (2019)
On Non-ergodic Volterra Cubic Stochastic OperatorsQualitative Theory of Dynamical Systems, 18
-
U. Jamilov, M. Scheutzow, M. Wilke-Berenguer (2014)
On the random dynamics of Volterra quadratic operatorsErgodic Theory and Dynamical Systems, 37
-
U. U. Jamilov, A. Reinfelds (2021)
A family of Volterra cubic stochastic operatorsJ. Convex Anal., 28
-
N. Ganikhodzhaev, D. Zanin (2004)
On a necessary condition for the ergodicity of quadratic operators defined on the two-dimensional simplexRussian Mathematical Surveys, 59
-
U. Jamilov, M. Ladra (2017)
On Identically Distributed non-Volterra Cubic Stochastic OperatorJournal of Applied Nonlinear Dynamics, 1
-
U. Jamilov, M. Ladra (2016)
Non-Ergodicity of Uniform Quadratic Stochastic OperatorsQualitative Theory of Dynamical Systems, 15
-
F. Mukhamedov, U. Jamilov, A. Pirnapasov (2019)
On Nonergodic Uniform Lotka–Volterra OperatorsMathematical Notes, 105
-
R. Robinson (2004)
An Introduction to Dynamical Systems: Continuous and Discrete -
Erica Chauvet, J. Paullet, J. Previte, Zac Walls (2002)
A Lotka-Volterra Three-species Food ChainMathematics Magazine, 75
-
A. Homburg, Uygun Jamilov, Michael Scheutzow (2018)
Asymptotics for a class of iterated random cubic operatorsNonlinearity, 32
-
(2004)
Khamraev, “On cubic operators of Volterra type, -
David Klarwer (2010)
A MODEL FOR POPULATION GROWTH -
H. Freedman, P. Waltman (1977)
Mathematical analysis of some three-species food-chain modelsBellman Prize in Mathematical Biosciences, 33
-
U. Jamilov, A. Khamraev, M. Ladra (2017)
On a Volterra Cubic Stochastic OperatorBulletin of Mathematical Biology, 80
-
U. Rozikov, A. Khamraev (2004)
On Cubic Operators Defined on Finite-Dimensional SimplexesUkrainian Mathematical Journal, 56
-
F. Mukhamedov, A. Embong, A. Rosli (2017)
Orthogonal-preserving and surjective cubic stochastic operatorsAnnals of Functional Analysis, 8
-
M Zakharevich (1978)
ON THE BEHAVIOUR OF TRAJECTORIES AND THE ERGODIC HYPOTHESIS FOR QUADRATIC MAPPINGS OF A SIMPLEXRussian Mathematical Surveys, 33
-
N. Ganikhodzhaev, U. Zhamilov, R. Mukhitdinov (2014)
Nonergodic Quadratic Operators for a Two-Sex PopulationUkrainian Mathematical Journal, 65
-
H. Freedman, P. Waltman (1984)
Persistence in models of three interacting predator-prey populationsBellman Prize in Mathematical Biosciences, 68
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2021
- ISSN
- 1995-0802
- eISSN
- 1818-9962
- DOI
- 10.1134/s1995080221120222
- Publisher site
- See Article on Publisher Site
Abstract
In present paper we consider a family of discrete time Kolmogorov systems of three interaction population depending on a parameter \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta$$\end{document}. We show that there is the critic value \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta^{*}$$\end{document} of parameter \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta$$\end{document} such that for \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta\in(\theta^{*},1]$$\end{document} this evolution operator is a non-ergodic transformation and for \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta\in[0,\theta^{*})$$\end{document} it has property being regular. We give some biological interpretations of our results.
Journal
Lobachevskii Journal of Mathematics – Springer Journals
Published: Dec 1, 2021
Keywords: cubic stochastic operator; Volterra operator; non-Volterra operator; regular and non-regular operator