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Lyapunov functions and dynamics of infinite dimensional volterra operators

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

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Official URL: http://dx.doi.org/10.1016/j.chaos.2023.113625

Abstract

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.

Item Type:Article
Uncontrolled Keywords:Infinite dimensional, Limiting set, Lyapunov function, Quadratic stochastic operators
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:105876
Deposited By: Widya Wahid
Deposited On:20 May 2024 07:24
Last Modified:20 May 2024 07:24

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