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^*

^*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلة › Article › مراجعة النظراء

22 اقتباسات (Scopus)

ملخص

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.

اللغة الأصلية	English
الصفحات (من إلى)	342-352
عدد الصفحات	11
دورية	Applied Mathematics and Computation
مستوى الصوت	180
رقم الإصدار	1
المعرِّفات الرقمية للأشياء	https://doi.org/10.1016/j.amc.2005.12.016
حالة النشر	Published - سبتمبر 1 2006
منشور خارجيًا	نعم

ASJC Scopus subject areas

???subjectarea.asjc.2600.2605???
???subjectarea.asjc.2600.2604???

الوصول إلى المستند

10.1016/j.amc.2005.12.016

الملفات والروابط الأخرى

قم بذكر هذا

@article{76470754dba44086a6632485dfc0b665,

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",

year = "2006",

month = sep,

day = "1",

doi = "10.1016/j.amc.2005.12.016",

language = "English",

volume = "180",

pages = "342--352",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

number = "1",

}

TY - JOUR

T1 - On the periodic logistic equation

AU - AlSharawi, Ziyad

AU - Angelos, James

PY - 2006/9/1

Y1 - 2006/9/1

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

UR - http://www.scopus.com/inward/record.url?scp=33748287043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748287043&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2005.12.016

DO - 10.1016/j.amc.2005.12.016

M3 - Article

AN - SCOPUS:33748287043

SN - 0096-3003

VL - 180

SP - 342

EP - 352

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

On the periodic logistic equation

ملخص

ASJC Scopus subject areas

الوصول إلى المستند

الملفات والروابط الأخرى

بصمة

قم بذكر هذا