### Abstract

We show that the p-periodic logistic equation x_{n+1} = μ_{n mod p}x_{n}(1 - x_{n}) has cycles (periodic solutions) of minimal periods 1, p, 2p, 3p, ... Then we extend Singer's theorem to periodic difference equations, and use it to show the p-periodic logistic equation has at most p stable cycles. Also, we present computational methods investigating the stable cycles in case p = 2 and 3.

Original language | English |
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Pages (from-to) | 342-352 |

Number of pages | 11 |

Journal | Applied Mathematics and Computation |

Volume | 180 |

Issue number | 1 |

DOIs | |

Publication status | Published - Sep 1 2006 |

### Keywords

- Attractors
- Logistic map
- Non-autonomous
- Periodic solutions
- Singer's theorem

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

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## Cite this

AlSharawi, Z., & Angelos, J. (2006). On the periodic logistic equation.

*Applied Mathematics and Computation*,*180*(1), 342-352. https://doi.org/10.1016/j.amc.2005.12.016