otka-Volterra Dynamics on S 3 with a Partially Oriented Interaction Graph

Nishonboyev, Sanjar

Ўзбекистон Миллий университети хабарлари · 2026-yil

Annotatsiya

We study a five-parameter Lotka–Volterra quadratic stochastic operator on the three-dimensional simplex S 3 in the degenerate case ce = ad. The corresponding skew-symmetric matrix hasexactly one zero interaction coefficient, and its partially oriented interaction graph contains two strongthree-vertex subtournaments. On the fixed labelled vertex set {1,2,3,4}, the isomorphism class of thisgraph contains exactly twelve labelled realizations. The degeneracy reduces the four coordinate growthforms to two independent linear forms. We determine the complete fixed-point set, prove that the kernelintersects the simplex in a segment of fixed points, construct the six non-empty signature polytopes andtheir adjacency cycle, and describe the admissible forward and backward crossing directions. We also proveconvergence of global negative trajectories contained in the relative interior to unique points of the fixedsegment and compute the Jacobian spectrum along that segment, including explicit eigenvalues and eigen-vectors at its endpoints.

Maqola ma’lumotlari
MualliflarNishonboyev, Sanjar
JurnalЎзбекистон Миллий университети хабарлари
NashriyotЎзбекистон Миллий университети
ISSN2181-7324, 3093-8996
Nashr sanasi2026-10-07
Jild2
Son2.3
Betlar153-163
TilIngliz
Ilmiy sohaKimyo
Indeksga qo‘shilgan2026-10-08

Maqolaning asl sahifasi

Kalit so‘zlar

Lotka–Volterra operator, simplex, partially oriented graph, strong tournament, fixed point, signature, convex polytope, trajectory, Jacobian spectrum.

Ilmiy soha

Kimyo

Iqtibos keltirish

APANishonboyev, Sanjar (2026). otka-Volterra Dynamics on S 3 with a Partially Oriented Interaction Graph. Ўзбекистон Миллий университети хабарлари, 2(2.3), 153-163. https://journals.nuu.uz/index.php/actanuuz/article/view/15263
GOST (OAK)Nishonboyev, Sanjar otka-Volterra Dynamics on S 3 with a Partially Oriented Interaction Graph // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 153-163.
MLANishonboyev, Sanjar. “otka-Volterra Dynamics on S 3 with a Partially Oriented Interaction Graph.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 153-163, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15263
ChicagoNishonboyev, Sanjar. “otka-Volterra Dynamics on S 3 with a Partially Oriented Interaction Graph.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 153-163 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15263
HarvardNishonboyev, Sanjar (2026) ‘otka-Volterra Dynamics on S 3 with a Partially Oriented Interaction Graph’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 153-163. https://journals.nuu.uz/index.php/actanuuz/article/view/15263
BibTeX
@article{nishonboyevsanjar2026,
  title = {otka-Volterra Dynamics on S 3 with a Partially Oriented Interaction Graph},
  author = {Nishonboyev, Sanjar},
  journal = {Ўзбекистон Миллий университети хабарлари},
  year = {2026},
  volume = {2},
  number = {2.3},
  pages = {153-163},
  url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15263}
}

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