On the periodic logistic equation

Ziyad AlSharawi, James Angelos

Research output: Contribution to journalArticle

19 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)342-352
Number of pages11
JournalApplied Mathematics and Computation
Volume180
Issue number1
DOIs
Publication statusPublished - 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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