Periodic orbits in periodic discrete dynamics

Ziyad AlSharawi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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
Issue number8
Publication statusPublished - Oct 2008


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

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


Dive into the research topics of 'Periodic orbits in periodic discrete dynamics'. Together they form a unique fingerprint.

Cite this