The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator
Not available
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Master's thesis |
| Language: | English |
| Published: |
Universiti Teknologi Malaysia
2025
|
| Subjects: | |
| Online Access: | https://utmik.utm.my/handle/123456789/41870 |
| Abstract | Abstract here |
| _version_ | 1854934102597173248 |
|---|---|
| author | Nur Natasha Lim Boon Chye @ Mohd. Hairie Lim |
| author2 | Ahmad Fadillah Embong, supervisor |
| author_facet | Ahmad Fadillah Embong, supervisor Nur Natasha Lim Boon Chye @ Mohd. Hairie Lim |
| author_sort | Nur Natasha Lim Boon Chye @ Mohd. Hairie Lim |
| description | Not available |
| format | Master's thesis |
| id | utm-123456789-41870 |
| institution | Universiti Teknologi Malaysia |
| language | English |
| publishDate | 2025 |
| publisher | Universiti Teknologi Malaysia |
| record_format | dspace |
| record_pdf | Abstract |
| spelling | utm-123456789-418702025-08-20T22:32:24Z The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator Nur Natasha Lim Boon Chye @ Mohd. Hairie Lim Ahmad Fadillah Embong, supervisor Science Not available Any sequence that is formed from the iteration of a certain operator is known as a dynamical system. For instance, in biological point of view, the dynamics of a population represent the changes of the species’ distribution over the time in the considered population. Thus, it is a particular interest to know what happen to the distribution of the traits in long run. One of the main problems in non-linear operator theory is to study their asymptotic behaviour such as regular, ergodic, or chaos. Even for the case of quadratic operator, this problem is not fully solved. This research is limited on quadratic stochastic operators (QSOs). There are many classes of QSOs such as Volterra QSOs, strictly non-Volterra QSOs, orthogonal preserving QSOs, and centered QSOs. However, none of the introduced classes cover the whole set of QSOs. Therefore, a new class of QSOs is introduced in this research, namely b-bistochastic- Volterra QSOs or simply bV-QSOs. In this research, the canonical forms of bV-QSOs defined on one and two-dimensional simplices are provided. Fixed points are obtained from the canonical form of bV-QSO on one-dimensional simplex and then classified into attracting, repelling, saddle, and non-hyperbolic by applying Jacobian matrix. Then, by using the constructed Lyapunov functions, the omega limiting set can be described, which answers one of the main problems in a dynamical system. The same procedures are applied for bV-QSOs on two-dimensional simplex. In this research, the genetic algebras generated by bV-QSOs is given and the non-associativity of the genetic algebras defined on two dimensions is provided by checking the properties on the standard basis. The results obtained in this study contribute to the advancement of knowledge in the theory of non-linear operator. zulraizam UTM 115 p. Thesis (Master of Philosophy (Mathematics)) - Universiti Tekbologi Malaysia, 2023 2025-03-10T03:07:41Z 2025-03-10T03:07:41Z 2023 Master's thesis https://utmik.utm.my/handle/123456789/41870 vital:153640 valet-20231011-085310 ENG Closed Access UTM Complete Unpublished Completion application/pdf Universiti Teknologi Malaysia |
| spellingShingle | Science Nur Natasha Lim Boon Chye @ Mohd. Hairie Lim The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator |
| thesis_level |
Master
|
| title | The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator |
| title_full | The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator |
| title_fullStr | The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator |
| title_full_unstemmed | The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator |
| title_short | The dynamics and genetic algebra associated with b-bistochastic-volterra quadratic stochastic operator |
| title_sort | dynamics and genetic algebra associated with b bistochastic volterra quadratic stochastic operator |
| topic | Science |
| url | https://utmik.utm.my/handle/123456789/41870 |
| work_keys_str_mv | AT nurnatashalimboonchyemohdhairielim thedynamicsandgeneticalgebraassociatedwithbbistochasticvolterraquadraticstochasticoperator AT nurnatashalimboonchyemohdhairielim dynamicsandgeneticalgebraassociatedwithbbistochasticvolterraquadraticstochasticoperator |