Cyclic R 2 (m) Lotka–Volterra Operators on Simplices: Classification on S 4 and Global Dynamics for Odd m

Akhmedova, Dilafruz

Ўзбекистон Миллий университети хабарлари · 2026-yil

Annotatsiya

We study discrete Lotka–Volterra operators V : S m−1 → S m−1 whose interactiongraph is the 2-regular cycle C m , referred to as R 2 (m) configurations. For m = 5 (the simplex S 4 )we classify all orientation patterns under the dihedral group D 5 via Burnside’s lemma, obtainingexactly four isomorphism classes (I)–(IV). For each class we determine the P → Q repeller–attractorstructure, describe invariant polytopes via coordinate signatures, and prove global convergence oftrajectories. For general odd m ≥ 3 we prove that the directed-cycle operator possesses a uniqueinterior fixed point M, construct an explicit Lyapunov function ϕ M , and show that every non-fixedinterior trajectory converges to the boundary in forward time while its α-limit set is {M}.

Maqola ma’lumotlari
MualliflarAkhmedova, Dilafruz
JurnalЎзбекистон Миллий университети хабарлари
NashriyotЎзбекистон Миллий университети
ISSN2181-7324, 3093-8996
Nashr sanasi2026-10-06
Jild2
Son2.3
Betlar16-25
TilIngliz
Indeksga qo‘shilgan2026-10-07

Maqolaning asl sahifasi

Kalit so‘zlar

discrete Lotka–Volterra operator; simplex; cyclic graph; Burnside’s lemma; coordinate signature; Lyapunov function; trajectory route; α- and ω-limit sets.

Iqtibos keltirish

APAAkhmedova, Dilafruz (2026). Cyclic R 2 (m) Lotka–Volterra Operators on Simplices: Classification on S 4 and Global Dynamics for Odd m. Ўзбекистон Миллий университети хабарлари, 2(2.3), 16-25. https://journals.nuu.uz/index.php/actanuuz/article/view/15238
GOST (OAK)Akhmedova, Dilafruz Cyclic R 2 (m) Lotka–Volterra Operators on Simplices: Classification on S 4 and Global Dynamics for Odd m // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 16-25.
MLAAkhmedova, Dilafruz. “Cyclic R 2 (m) Lotka–Volterra Operators on Simplices: Classification on S 4 and Global Dynamics for Odd m.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 16-25, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15238
ChicagoAkhmedova, Dilafruz. “Cyclic R 2 (m) Lotka–Volterra Operators on Simplices: Classification on S 4 and Global Dynamics for Odd m.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 16-25 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15238
HarvardAkhmedova, Dilafruz (2026) ‘Cyclic R 2 (m) Lotka–Volterra Operators on Simplices: Classification on S 4 and Global Dynamics for Odd m’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 16-25. https://journals.nuu.uz/index.php/actanuuz/article/view/15238
BibTeX
@article{akhmedovadilafruz2026,
  title = {Cyclic R 2 (m) Lotka–Volterra Operators on Simplices: Classification on S 4 and Global Dynamics for Odd m},
  author = {Akhmedova, Dilafruz},
  journal = {Ўзбекистон Миллий университети хабарлари},
  year = {2026},
  volume = {2},
  number = {2.3},
  pages = {16-25},
  url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15238}
}

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