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Article · Uzbek Mathematical Journal · August 30, 2024
The dynamics of a separable cubic operator
Abstract
In the present paper, we consider cubic stochastic operators defined on a finite-dimensional simplex. These operators are called separable cubic stochastic operators and depend on a permutation and four parameters. We show that for any permutation, except the identity permutation, any trajectory of corresponding operators converges to a periodic trajectory. Any trajectory of the operator corresponding to the identity permutation converges to a fixed point.
Mathematical Dynamics and Fractalsp-Adic Analysis and Mathematical PhysicsAdvanced Differential Equations and Dynamical Systemspermutationsperiodic trajectoriesfixed points
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