an:05072721
Zbl 1109.90010
AlSharawi, Ziyad; Angelos, James
On the periodic logistic equation
EN
Appl. Math. Comput. 180, No. 1, 342-352 (2006).
00186886
2006
j
90B06 39A11 37C25 37C70
logistic map; non-autonomous; periodic solutions; Singer's theorem; attractors
Summary: We show that the \(p\)-periodic logistic equation \(x_{n+1} = \mu _{n\,\text{mod\,} p}x_{n}(1 - x_{n})\) has cycles (periodic solutions) of minimal periods \(1, p, 2p, 3p, \dots\) 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.