SEPARABLE CUBIC STOCHASTIC OPERATORS
Keywords:
cubic stochastic operator, separable cubic stochastic operatorAbstract
In this paper, we study the trajectory of a separable cubic stochastic operator on a two-dimensional simplex, which naturally arises in the study of certain problems of population biology. In the simplest problem of population genetics, a biological system of a finite set consisting of n species 1, 2, …, n is considered.
References
S. Bernstein, Solution of a mathematical problem connected with the theory of heredity}, Ann. Math. Stat. 13(1) (1942), pp. 53--61. DOI:10.1214/aoms/1177731642.
R. R. Davronov, U. U. Jamilov(Zhamilov), and M. Ladra, Conditional cubic stochastic operator, J. Differ. Equ. Appl. 21(12) (2015), pp. 1163--1170. DOI:10.1080/10236198.2015.1062481.
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, in Studies in Nonlinearity, Westview Press, Boulder, CO, 2003.
R. N. Ganikhodzhaev, Quadratic stochastic operators, Lyapunov functions and tournaments, Sb. Math.76(2) (1993), pp. 489--506. DOI:10.1070/SM1993v076n02ABEH003423.
R. N. Ganikhodzhaev and D. B. Eshmamatova, Quadratic automorphisms of a simplex and the asymptotic behavior of their trajectories, Vladikavkaz. Mat. Zh. 8(2) (2006), pp. 12--28.
A. Yu. Khamraev, On cubic operators of Volterra type, Uzbek. Mat. Zh. 2004(2) (2004), pp. 79--84. (in Russian).
U. A. Rozikov, S. Nazir, Separable Quadratic Stochastic Operators, Lobschevskii J. Math. (3), 215(2010), pp. 215-221. DOI: 10.1134/S1995080210030030.
U. A. Rozikov, A. Zada, On a Class of Separable Quadratic Stochastic Operators, Lobschevskii J. Math. (4), 32(2011), pp. 385--394. DOI: 10.1134/S1995080211040196.
R. R. Davronov, U. U. Jamilov(Zhamilov), and M. Ladra, Conditional cubic stochastic operator, J. Differ. Equ. Appl. 21(12) (2015), pp. 1163--1170. DOI:10.1080/10236198.2015.1062481.
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, in Studies in Nonlinearity, Westview Press, Boulder, CO, 2003.
R. N. Ganikhodzhaev, Quadratic stochastic operators, Lyapunov functions and tournaments, Sb. Math.76(2) (1993), pp. 489--506. DOI:10.1070/SM1993v076n02ABEH003423.
R. N. Ganikhodzhaev and D. B. Eshmamatova, Quadratic automorphisms of a simplex and the asymptotic behavior of their trajectories, Vladikavkaz. Mat. Zh. 8(2) (2006), pp. 12--28.
A. Yu. Khamraev, On cubic operators of Volterra type, Uzbek. Mat. Zh. 2004(2) (2004), pp. 79--84. (in Russian).
U. A. Rozikov, S. Nazir, Separable Quadratic Stochastic Operators, Lobschevskii J. Math. (3), 215(2010), pp. 215-221. DOI: 10.1134/S1995080210030030.
U. A. Rozikov, A. Zada, On a Class of Separable Quadratic Stochastic Operators, Lobschevskii J. Math. (4), 32(2011), pp. 385--394. DOI: 10.1134/S1995080211040196.
Downloads
Published
2023-12-20
How to Cite
Baratov B. S. (2023). SEPARABLE CUBIC STOCHASTIC OPERATORS. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 4(12), 81–89. Retrieved from https://cajmtcs.casjournal.org/index.php/CAJMTCS/article/view/579
Issue
Section
Articles
