### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

*Applied Mathematics and Computation*,

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

**On the periodic logistic equation.** / AlSharawi, Ziyad; Angelos, James.

Research output: Contribution to journal › Article

*Applied Mathematics and Computation*, vol. 180, no. 1, pp. 342-352. https://doi.org/10.1016/j.amc.2005.12.016

}

TY - JOUR

T1 - On the periodic logistic equation

AU - AlSharawi, Ziyad

AU - Angelos, James

PY - 2006/9/1

Y1 - 2006/9/1

N2 - We show that the p-periodic logistic equation xn+1 = μn mod pxn(1 - xn) 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.

AB - We show that the p-periodic logistic equation xn+1 = μn mod pxn(1 - xn) 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.

KW - Attractors

KW - Logistic map

KW - Non-autonomous

KW - Periodic solutions

KW - Singer's theorem

UR - http://www.scopus.com/inward/record.url?scp=33748287043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748287043&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2005.12.016

DO - 10.1016/j.amc.2005.12.016

M3 - Article

AN - SCOPUS:33748287043

VL - 180

SP - 342

EP - 352

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 1

ER -