Abstract
As is known [3], each quadratic stochastic operator of Volterra type acting on a finite-dimensional simplex defines a certain tournament, the properties of which make it possible to study the asymptotic behavior of the trajectories of this Volterra operator. In this paper, we introduce the concept of a homogeneous tournament and study the dynamic properties of Volterra operators corresponding to homogeneous tournaments in the simplex S4.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 4, Science — Technology — Education — Mathematics — Medicine, 2022.
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Tadzhieva, M.A., Eshmamatova, D.B. & Ganikhodzhaev, R.N. Volterra-Type Quadratic Stochastic Operators with a Homogeneous Tournament. J Math Sci 278, 546–556 (2024). https://doi.org/10.1007/s10958-024-06937-0
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DOI: https://doi.org/10.1007/s10958-024-06937-0