### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

*Computers and Mathematics with Applications*,

*56*(8), 1966-1974. https://doi.org/10.1016/j.camwa.2008.04.020

**Periodic orbits in periodic discrete dynamics.** / AlSharawi, Ziyad.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 56, no. 8, pp. 1966-1974. https://doi.org/10.1016/j.camwa.2008.04.020

}

TY - JOUR

T1 - Periodic orbits in periodic discrete dynamics

AU - AlSharawi, Ziyad

PY - 2008/10

Y1 - 2008/10

N2 - 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.

AB - 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.

KW - Combinatorial dynamics

KW - Periodic difference equations

KW - Periodic orbits

KW - Population models

UR - http://www.scopus.com/inward/record.url?scp=51049093793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51049093793&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2008.04.020

DO - 10.1016/j.camwa.2008.04.020

M3 - Article

VL - 56

SP - 1966

EP - 1974

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 8

ER -