Periodic solutions of the second order quadratic rational difference equation xn+1 = α/(1+xn)xn-1

Inese Bula

doi:10.1007/978-3-662-52927-0_3

Periodic solutions of the second order quadratic rational difference equation x_n+1 = α/(1+x_n)x_n-1

Inese Bula^*

^*Corresponding author for this work

Department of Mathematics

University of Latvia

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › Research › peer-review

1 Citation (Scopus)

Abstract

The aim of this article is to investigate the periodic nature of solutions of a rational difference equation x_n+1 = α/(1+x_n)x_n-1 We explore Open Problem 3.3 given in Amleh et al. (Int J Differ Equ 3(1):1–35, 2008, [2]) that requires to determine all periodic solutions of the equation (*).We conclude that for the equation (*) there are no periodic solution with prime period 3 and 4. Period 7 is first period for which exists nonnegative parameter α and nonnegative initial conditions.

Original language	English
Title of host publication	Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012
Editors	Jim M. Cushing, Alberto A. Pinto, Saber Elaydi, Lluis Alseda i Soler
Publisher	Springer New York LLC
Pages	29-47
Number of pages	19
ISBN (Print)	9783662529263
DOIs	https://doi.org/10.1007/978-3-662-52927-0_3
Publication status	Published - 2016
Event	18th International Conference on Difference Equations and Applications, ICDEA 2012 - Barcelona, Spain Duration: 23 Jul 2012 → 27 Jul 2012

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	180
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	18th International Conference on Difference Equations and Applications, ICDEA 2012
Country/Territory	Spain
City	Barcelona
Period	23/07/12 → 27/07/12

Keywords

Difference equation
Equilibrium point
Periodic solution
Rational difference equation

Access to Document

10.1007/978-3-662-52927-0_3

Cite this

Bula, I. (2016). Periodic solutions of the second order quadratic rational difference equation x_n+1 = α/(1+x_n)x_n-1. In J. M. Cushing, A. A. Pinto, S. Elaydi, & L. A. i Soler (Eds.), Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012 (pp. 29-47). (Springer Proceedings in Mathematics and Statistics; Vol. 180). Springer New York LLC. https://doi.org/10.1007/978-3-662-52927-0_3

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title = "Periodic solutions of the second order quadratic rational difference equation xn+1 = α/(1+xn)xn-1",

abstract = "The aim of this article is to investigate the periodic nature of solutions of a rational difference equation xn+1 = α/(1+xn)xn-1 We explore Open Problem 3.3 given in Amleh et al. (Int J Differ Equ 3(1):1–35, 2008, [2]) that requires to determine all periodic solutions of the equation (*).We conclude that for the equation (*) there are no periodic solution with prime period 3 and 4. Period 7 is first period for which exists nonnegative parameter α and nonnegative initial conditions.",

keywords = "Difference equation, Equilibrium point, Periodic solution, Rational difference equation",

author = "Inese Bula",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2016.; 18th International Conference on Difference Equations and Applications, ICDEA 2012 ; Conference date: 23-07-2012 Through 27-07-2012",

year = "2016",

doi = "10.1007/978-3-662-52927-0\_3",

language = "English",

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pages = "29--47",

editor = "Cushing, \{Jim M.\} and Pinto, \{Alberto A.\} and Saber Elaydi and \{i Soler\}, \{Lluis Alseda\}",

booktitle = "Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012",

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Bula, I 2016, Periodic solutions of the second order quadratic rational difference equation x_n+1 = α/(1+x_n)x_n-1. in JM Cushing, AA Pinto, S Elaydi & LA i Soler (eds), Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012. Springer Proceedings in Mathematics and Statistics, vol. 180, Springer New York LLC, pp. 29-47, 18th International Conference on Difference Equations and Applications, ICDEA 2012, Barcelona, Spain, 23/07/12. https://doi.org/10.1007/978-3-662-52927-0_3

Periodic solutions of the second order quadratic rational difference equation x_n+1 = α/(1+x_n)x_n-1. / Bula, Inese.
Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012. ed. / Jim M. Cushing; Alberto A. Pinto; Saber Elaydi; Lluis Alseda i Soler. Springer New York LLC, 2016. p. 29-47 (Springer Proceedings in Mathematics and Statistics; Vol. 180).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › Research › peer-review

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N2 - The aim of this article is to investigate the periodic nature of solutions of a rational difference equation xn+1 = α/(1+xn)xn-1 We explore Open Problem 3.3 given in Amleh et al. (Int J Differ Equ 3(1):1–35, 2008, [2]) that requires to determine all periodic solutions of the equation (*).We conclude that for the equation (*) there are no periodic solution with prime period 3 and 4. Period 7 is first period for which exists nonnegative parameter α and nonnegative initial conditions.

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KW - Equilibrium point

KW - Periodic solution

KW - Rational difference equation

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