Periodic orbits in periodic discrete dynamics

Ziyad AlSharawi

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We study the combinatorial structure of periodic orbits of nonautonomous difference equations xn + 1 = fn (xn) in a periodically fluctuating environment. We define the Γ-set to be the set of minimal periods that are not multiples of the phase period. We show that when the functions fn are rational functions, the Γ-set is a finite set. In particular, we investigate several mathematical models of single-species without age structure, and find that periodic oscillations are influenced by periodic environments to the extent that almost all periods are divisors or multiples of the phase period.

Original languageEnglish
Pages (from-to)1966-1974
Number of pages9
JournalComputers and Mathematics with Applications
Volume56
Issue number8
DOIs
Publication statusPublished - Oct 2008

Keywords

  • Combinatorial dynamics
  • Periodic difference equations
  • Periodic orbits
  • Population models

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

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