### Abstract

We study the combinatorial structure of periodic orbits of nonautonomous difference equations x_{n + 1} = f_{n} (x_{n}) 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 f_{n} 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 language | English |
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Pages (from-to) | 1966-1974 |

Number of pages | 9 |

Journal | Computers and Mathematics with Applications |

Volume | 56 |

Issue number | 8 |

DOIs | |

Publication status | Published - 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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## Cite this

AlSharawi, Z. (2008). Periodic orbits in periodic discrete dynamics.

*Computers and Mathematics with Applications*,*56*(8), 1966-1974. https://doi.org/10.1016/j.camwa.2008.04.020