Periodicity of the Discrete Dynamical Systems

N. P. Mahmatqobilov

doi:10.5281/

Authors

N. P. Mahmatqobilov Karshi state university Department of Mathematical analysis and differential equations Author

DOI:

https://doi.org/10.5281/

Keywords:

Cubic stochastic operator, finite-dimensional simplex, permutation, fixed point

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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