On Dynamics of Cubic Stochastic Operators
Main Article Content
Abstract
In this paper, we consider a class of cubic stochastic operators defined on a finite-dimensional simplex. Namely, cubic stochastic operators that have the form of a product of three linear operators defined on a simplex.
Article Details
Section
How to Cite
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.
R.~Ganikhodzhaev, F.~Mukhamedov, and U.~Rozikov, Quadratic stochastic operators and processes: Results and open problems, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14(2) (2011), pp. 279--335.
A.~J. Homburg, U.~U.~Jamilov, and M.~Scheutzow, Asymptotics for a class of iterated random cubic operators, Nonlinearity 32(10) (2019), pp. 3646--3660. DOI:10.1088/1361-6544/ab1f24.
U.~A.~Rozikov, A.~Yu.~Khamraev}, On cubic operators defined on finite-dimensional simplices, Ukr Math. J. 56(10), (2004) pp. 1699-1711.
U.~A.~Rozikov, S.~Nazir}, emph{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.