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On a Non-Volterra Cubic Stochastic Operator

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Abstract

In the present paper we consider a family of non-Volterra cubic stochastic operators depending on a parameter \(\theta\) and study their trajectory behaviors. We find all fixed and periodic points for a non-Volterra cubic stochastic operator on the two-dimensional simplex. We show that if \(-1\leq\theta<0\) then any trajectory of a cubic stochastic operator converges to the center of the simplex, if \(\theta=0\) then the corresponding cubic stochastic operator is the identity map, if \(0<\theta\leq 1\) then the set of limit points of trajectories of a cubic stochastic operator of an initial point is an infinite subset of the boundary of the two-dimensional simplex.

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Authors and Affiliations

  1. V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 100174, Tashkent, Uzbekistan

    U. U. Jamilov

  2. Akfa University, 100095, Tashkent, Uzbekistan

    U. U. Jamilov

  3. National University of Uzbekistan, 100174, Tashkent, Uzbekistan

    U. U. Jamilov

  4. Faculty of Mathematics, National University of Uzbekistan, 100174, Tashkent, Uzbekistan

    K. A. Kurganov

Authors
  1. U. U. Jamilov
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  2. K. A. Kurganov
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Correspondence to U. U. Jamilov or K. A. Kurganov.

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(Submitted by S. N. Tronin)

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Jamilov, U.U., Kurganov, K.A. On a Non-Volterra Cubic Stochastic Operator. Lobachevskii J Math 42, 2800–2807 (2021). https://doi.org/10.1134/S1995080221120155

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  • DOI: https://doi.org/10.1134/S1995080221120155

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