Periodicity of the Discrete Dynamical Systems
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Abstract
In the present paper, we consider cubic stochastic operators defined on a finite-dimensional simplex, which are depend on a permutation. We showed that for any permutation , except the identity permutation, the trajectories of the corresponding operators converges to a periodic trajectory. The trajectories of the operator corresponding to the identity permutation converge to a fixed point.
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R.L.Devaney. An introduction to chaotic dynamical systems, Studies in Nonlinearity, Westview Press, Boulder, CO, 2003, reprint of the second (1989) edition.
U.U.Jamilov, A.Yu.Khamraev, M. Ladra, On a Volterra cubic stochastic operator, Bull. Math. Biol. 80 (2) (2018) 319-334.
U.A.Rozikov, A.Yu.Khamraev, On cubic operators defined on finite-dimensional simplices, Ukrainian Math. J. 56 (10) (2004) 1699-1711.
U.A.Rozikov, S.Nazir, Separable quadratic stochastic operators. Lobachevskii J. Math. 31 (2010) 215-221.