Geodesic
Volterra-type quadratic stochastic operators with a homogeneous tournament
Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 783-794

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As is known [1], 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 $S^{4}$. 
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     author = {M. A. Tadzhieva and D. B. Eshmamatova and R. N. Ganikhodzhaev},
     title = {Volterra-type quadratic stochastic operators with a homogeneous tournament},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {783--794},
     publisher = {mathdoc},
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     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a9/}
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M. A. Tadzhieva; D. B. Eshmamatova; R. N. Ganikhodzhaev. Volterra-type quadratic stochastic operators with a homogeneous tournament. Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 783-794. http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a9/