Lyapunov functions and dynamics of infinite dimensional Volterra operators

Ahmad Fadillah Embong, Farrukh Mukhamedov

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number113625
JournalChaos, Solitons and Fractals
Volume173
DOIs
Publication statusPublished - Aug 2023

Keywords

  • Infinite dimensional
  • Limiting set
  • Lyapunov function
  • Quadratic stochastic operators

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics

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