On the periodic logistic equation

Ziyad AlSharawi; James Angelos

doi:10.1016/j.amc.2005.12.016

On the periodic logistic equation

Ziyad AlSharawi, James Angelos^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

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
Pages (from-to)	342-352
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	180
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2005.12.016
Publication status	Published - Sept 1 2006
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2005.12.016

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title = "On the periodic logistic equation",

abstract = "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.",

keywords = "Attractors, Logistic map, Non-autonomous, Periodic solutions, Singer's theorem",

author = "Ziyad AlSharawi and James Angelos",

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AU - Angelos, James

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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

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DO - 10.1016/j.amc.2005.12.016

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SP - 342

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

On the periodic logistic equation

Abstract

Keywords

ASJC Scopus subject areas

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