A many-loci system with evolution characterized by uncountable linear operators
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914960130441216 |
|---|---|
| author | Omirov, B. A. Rozikov, U. A. |
| author_facet | Omirov, B. A. Rozikov, U. A. |
| contents | This paper investigates the evolution of a multi-locus biological system. The evolution of such a system is described by a quadratic stochastic operator (QSO) defined on a simplex. We demonstrate that this QSO can be decomposed into an infinite series of linear operators, each of which maps certain invariant subsets of the simplex to themselves. Furthermore, the entire simplex is the union of these invariant subsets, enabling analytical examination of the dynamical systems produced by the QSO. Finding all limit points of the dynamical system generated by the QSO in terms of the limit points of the linear operators, we provide a comprehensive characterization of the many-loci population dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A many-loci system with evolution characterized by uncountable linear operators Omirov, B. A. Rozikov, U. A. Dynamical Systems 37N25, 92D10 This paper investigates the evolution of a multi-locus biological system. The evolution of such a system is described by a quadratic stochastic operator (QSO) defined on a simplex. We demonstrate that this QSO can be decomposed into an infinite series of linear operators, each of which maps certain invariant subsets of the simplex to themselves. Furthermore, the entire simplex is the union of these invariant subsets, enabling analytical examination of the dynamical systems produced by the QSO. Finding all limit points of the dynamical system generated by the QSO in terms of the limit points of the linear operators, we provide a comprehensive characterization of the many-loci population dynamics. |
| title | A many-loci system with evolution characterized by uncountable linear operators |
| topic | Dynamical Systems 37N25, 92D10 |
| url | https://arxiv.org/abs/2409.19687 |