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Publication

On the periodic logistic equation

Al-Sharawi, Ziyad
Angelos, James
Date
2006
Advisor
Type
Peer-Reviewed
Article
Preprint
Degree
Description
Abstract
We show that the 𝒑-periodic logistic equation π’³β‚™β‚Šβ‚ = ΞΌβ‚™ 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.