IDEMPOTENT O‘LCHOVLAR SIMPLEKSIDA ANIQLANGAN CHIZIQLI OPERATORLAR DINAMIKASINING EKOLOGIK MODELLASHTIRISHDAGI TATBIQI
DOI:
https://doi.org/10.5281/zenodo.20691666Keywords:
idempotent o‘lchovlar, chiziqli operatorlar, dinamik tizimlar, ekologik modellashtirish, populyatsiya dinamikasi, maxplus algebra, barqarorlik.Abstract
Ushbu maqolada idempotent o‘lchovlar simpleksida aniqlangan chiziqli operatorlarning dinamikasi ekologik
tizimlarni modellashtirishda qo‘llanilishi o‘rganiladi. Idempotent matematika asosida “maksimum-qo‘shish” (max-plus)
algebrasi yordamida populyatsiyalararo munosabatlar, resurs taqsimoti va ekologik muvozanat holatlari modellashtiriladi.
Operatorlarning ikki sinfi — nol qatorli (degenerativ) va permutatsion (siklik) xaritalar — ekologik jarayonlarning turli xil
ssenariylarini ifodalaydi. Har bir teorema uchun batafsil, qadam-baqadam isbotlar keltirilgan. Aniq misollar — Orolbo‘yi
mintaqasidagi turlararo munosabatlar va suv resurslarini taqsimlash masalalari asosida tahlil qilinadi. Olingan natijalar
ekologik tizimlarning barqarorligini bashorat qilish va optimallashtirish masalalarida qo‘llanilishi mumkin
References
Litvinov G.L., Maslov V.P. Idempotent Analysis and Its Applications. Dordrecht: Kluwer Academic
Publishers, 1997.
Rozikov U.A., Karimov M.M. Dynamics of Linear Maps of Idempotent Measures // Lobachevskii
Journal of Mathematics. 2013. Vol. 34. No. 1. P. 20–28.
Baccelli F., Cohen G., Olsder G.J., Quadrat J.P. Synchronization and Linearity: An Algebra for Discrete
Event Systems. New York: Wiley, 1992.
Kolokoltsov V.N., Maslov V.P. Idempotent Analysis and Its Applications. Dordrecht: Kluwer Academic
Publishers, 1997.
Cuninghame-Green R.A. Minimax Algebra. Berlin: Springer-Verlag, 1979.
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