# On the periodic logistic equation

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 language English 342-352 11 Applied Mathematics and Computation 180 1 https://doi.org/10.1016/j.amc.2005.12.016 Published - Sep 1 2006

### Fingerprint

Logistic Equation
Logistics
Cycle
Difference equations
Computational methods
Minimal Period
Computational Methods
Difference equation
Periodic Solution
Theorem

### Keywords

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

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics
• Numerical Analysis

### Cite this

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

In: Applied Mathematics and Computation, Vol. 180, No. 1, 01.09.2006, p. 342-352.

Research output: Contribution to journalArticle

AlSharawi, Ziyad ; Angelos, James. / On the periodic logistic equation. In: Applied Mathematics and Computation. 2006 ; Vol. 180, No. 1. pp. 342-352.
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