Trajectory Routes and Velocity-Signature Classification of Transitive and Mixed Lotka–Volterra Tournament Operators on S 3

Eshmamatova, Dilfuza, Nurboyev, Ilhombek

Ўзбекистон Миллий университети хабарлари · 2026-yil

Annotatsiya

We give a complete velocity-signature classification of two discrete Lotka–Volterra op-erators generated by fully oriented tournaments on the three-dimensional simplex S 3 : the transitivetournament T 1 and the mixed tournament T 2 , in which one vertex is dominated by all others whilethe remaining three vertices form a directed 3-cycle. The two matrices coincide in their first rowand column, so any difference in the resulting dynamics is attributable solely to the internal orderof the three subordinate strategies. Using the identity x 0k − x k= x k (Ax) k , we convert the sixteenformal sign patterns of Ax into systems of linear inequalities and classify all admissible ones for bothmodels, obtaining N(T 1 ) = 3 and N(T 2 ) = 7. For each operator we give the explicit convex-hulldomains (where tractable), the complete Jacobian spectrum at every vertex, a Lyapunov-type argu-ment for global convergence, the fixed-point set, and the evolutionary-game reading. Although bothoperators eliminate the same dominated strategy, T 1 converges to a single dominant vertex, whereasthe restriction of V 2 to the complementary invariant face coincides with the classical non-convergentthree-cycle Volterra operator.

Maqola ma’lumotlari
MualliflarEshmamatova, Dilfuza, Nurboyev, Ilhombek
JurnalЎзбекистон Миллий университети хабарлари
NashriyotЎзбекистон Миллий университети
ISSN2181-7324, 3093-8996
Nashr sanasi2026-10-07
Jild2
Son2.3
Betlar68-77
TilIngliz
Indeksga qo‘shilgan2026-10-08

Maqolaning asl sahifasi

Kalit so‘zlar

Lotka–Volterra operator, quadratic stochastic operator, tournament, simplex, velocity signature, convex polyhedron, evolutionary game theory, Lyapunov function.

Iqtibos keltirish

APAEshmamatova, Dilfuza, & Nurboyev, Ilhombek (2026). Trajectory Routes and Velocity-Signature Classification of Transitive and Mixed Lotka–Volterra Tournament Operators on S 3. Ўзбекистон Миллий университети хабарлари, 2(2.3), 68-77. https://journals.nuu.uz/index.php/actanuuz/article/view/15304
GOST (OAK)Eshmamatova, Dilfuza, Nurboyev, Ilhombek Trajectory Routes and Velocity-Signature Classification of Transitive and Mixed Lotka–Volterra Tournament Operators on S 3 // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 68-77.
MLAEshmamatova, Dilfuza, and Nurboyev, Ilhombek. “Trajectory Routes and Velocity-Signature Classification of Transitive and Mixed Lotka–Volterra Tournament Operators on S 3.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 68-77, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15304
ChicagoEshmamatova, Dilfuza, and Nurboyev, Ilhombek. “Trajectory Routes and Velocity-Signature Classification of Transitive and Mixed Lotka–Volterra Tournament Operators on S 3.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 68-77 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15304
HarvardEshmamatova, Dilfuza, and Nurboyev, Ilhombek (2026) ‘Trajectory Routes and Velocity-Signature Classification of Transitive and Mixed Lotka–Volterra Tournament Operators on S 3’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 68-77. https://journals.nuu.uz/index.php/actanuuz/article/view/15304
BibTeX
@article{eshmamatovadilfuza2026,
  title = {Trajectory Routes and Velocity-Signature Classification of Transitive and Mixed Lotka–Volterra Tournament Operators on S 3},
  author = {Eshmamatova, Dilfuza and Nurboyev, Ilhombek},
  journal = {Ўзбекистон Миллий университети хабарлари},
  year = {2026},
  volume = {2},
  number = {2.3},
  pages = {68-77},
  url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15304}
}

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