ON DYNAMICS OF A CUBIC STOCHASTIC OPERATORS IN
DOI:
https://doi.org/10.5281/zenodo.19812766Abstract
In this article, we study the Volterra cubic stochastic operator defined on a two-dimensional simplex. That is, we consider the cubic stochastic operator defined on a simplex. It is shown that for the Volterra cubic stochastic operator defined on a two-dimensional simplex, the vertices of the simplex are fixed points.
References
Devaney R.L. An introduction to chaotic dynamical systems, // Boulder, Stud. Nonlinearity, Westview Press, 2003.
Baratov, B.S., Jamilov, U.U. On separable cubic stochastic operators, // Qual. Theory Dyn. Syst. Vol 23, Issue 2, a.n. 93. 28 pages. (2024).
Baratov B. S. On dynamics of a separable cubic stochastic operator, // Bull. Inst. Math., Vol 6, Issue 1, pp. 17-25, (2023).
Rozikov U. A., Khamraev A. Yu. On cubic operators defined on finite-dimensional simplexes, // Ukrainian Math. J. Vol 56, Issue 10, pp. 223-228, (2004).
Rozikov U.A., Nazir S. Separable quadratic stochastic operators, // Lobachevskii J. Math. Vol 31, Issue 3, pp. 215-222, (2010).
Rozikov U.A., Zada A. On a class of separable quadratic stochastic operators, // Lobachevskii Jour. Math. Vol 32, Issue 4, pp. 397-406, (2011).
