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Lyapunov functions and dynamics of infinite dimensional volterra operators

The majority of research on quadratic stochastic operators (QSOs) was done on a finite-dimensional set of all probability distributions (also known as a simplex), thus it is intriguing to extend them for an infinite case. In particular, the infinite dimensional Volterra operators are discussed in th...

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Main Authors: Embong, Ahmad Fadillah, Mukhamedov, Farrukh
Format: Article
Published: Elsevier Ltd 2023
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/105876/
http://dx.doi.org/10.1016/j.chaos.2023.113625
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spelling my.utm.1058762024-05-20T07:24:37Z http://eprints.utm.my/105876/ Lyapunov functions and dynamics of infinite dimensional volterra operators Embong, Ahmad Fadillah Mukhamedov, Farrukh QA Mathematics The majority of research on quadratic stochastic operators (QSOs) was done on a finite-dimensional set of all probability distributions (also known as a simplex), thus it is intriguing to extend them for an infinite case. In particular, the infinite dimensional Volterra operators are discussed in the current paper. Due to the fact non-compactness of infinite dimensional simplex (unlike a finite case) makes the general study challenging, therefore, a sub-class of infinite dimensional Volterra operators is introduced. Furthermore, we construct Lyapunov functions which allow us to explore the dynamics of the introduced operators. Several examples are given with a full description of the limiting set. Elsevier Ltd 2023 Article PeerReviewed Embong, Ahmad Fadillah and Mukhamedov, Farrukh (2023) Lyapunov functions and dynamics of infinite dimensional volterra operators. Chaos, Solitons and Fractals, 173 (NA). NA-NA. ISSN 0960-0779 http://dx.doi.org/10.1016/j.chaos.2023.113625 DOI : 10.1016/j.chaos.2023.113625
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Embong, Ahmad Fadillah
Mukhamedov, Farrukh
Lyapunov functions and dynamics of infinite dimensional volterra operators
description The majority of research on quadratic stochastic operators (QSOs) was done on a finite-dimensional set of all probability distributions (also known as a simplex), thus it is intriguing to extend them for an infinite case. In particular, the infinite dimensional Volterra operators are discussed in the current paper. Due to the fact non-compactness of infinite dimensional simplex (unlike a finite case) makes the general study challenging, therefore, a sub-class of infinite dimensional Volterra operators is introduced. Furthermore, we construct Lyapunov functions which allow us to explore the dynamics of the introduced operators. Several examples are given with a full description of the limiting set.
format Article
author Embong, Ahmad Fadillah
Mukhamedov, Farrukh
author_facet Embong, Ahmad Fadillah
Mukhamedov, Farrukh
author_sort Embong, Ahmad Fadillah
title Lyapunov functions and dynamics of infinite dimensional volterra operators
title_short Lyapunov functions and dynamics of infinite dimensional volterra operators
title_full Lyapunov functions and dynamics of infinite dimensional volterra operators
title_fullStr Lyapunov functions and dynamics of infinite dimensional volterra operators
title_full_unstemmed Lyapunov functions and dynamics of infinite dimensional volterra operators
title_sort lyapunov functions and dynamics of infinite dimensional volterra operators
publisher Elsevier Ltd
publishDate 2023
url http://eprints.utm.my/105876/
http://dx.doi.org/10.1016/j.chaos.2023.113625
_version_ 1800082675927613440
score 13.15806

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