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^*

^*Šī darba korespondējošais autors

Matemātikas nodaļa

University of Latvia

Zinātniskās darbības rezultāts: Nodaļa grāmatā/enciklopēdijā/konferences krājumā › Konferences zinātniskais raksts › Pētniecība › koleģiāli recenzēts

1 Atsauce (Scopus)

Kopsavilkums

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.

Oriģinālvaloda	Angļu
Rīkotāja publikācijas nosaukums	Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012
Redaktori	Jim M. Cushing, Alberto A. Pinto, Saber Elaydi, Lluis Alseda i Soler
Izdevējs	Springer New York LLC
Lapas	29-47
Lapu skaits	19
ISBN (Drukātā versija)	9783662529263
DOIs	https://doi.org/10.1007/978-3-662-52927-0_3
Publikācijas statuss	Publicēts - 2016
Pasākums	18th International Conference on Difference Equations and Applications, ICDEA 2012 - Barcelona, Spānija Ilgums: 23 jūl. 2012 → 27 jūl. 2012

Publikāciju sērijas

Nosaukums	Springer Proceedings in Mathematics and Statistics
Sējums	180
ISSN (Drukātā versija)	2194-1009
ISSN (Elektroniskā versija)	2194-1017

Konference

Konference	18th International Conference on Difference Equations and Applications, ICDEA 2012
Valsts/Teritorija	Spānija
Pilsēta	Barcelona
Periods	23/07/12 → 27/07/12

Piekļuve Dokumentiem

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

Citi faili un saites

Saite uz publikāciju Scopus

Citēt šo

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

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

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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",

isbn = "9783662529263",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

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",

}

Bula, I 2016, Periodic solutions of the second order quadratic rational difference equation x_n+1 = α/(1+x_n)x_n-1. (kur) JM Cushing, AA Pinto, S Elaydi & LA i Soler (red.), Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012. Springer Proceedings in Mathematics and Statistics, sēj. 180, Springer New York LLC, lpp. 29-47, 18th International Conference on Difference Equations and Applications, ICDEA 2012, Barcelona, Spānija, 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. red. / Jim M. Cushing; Alberto A. Pinto; Saber Elaydi; Lluis Alseda i Soler. Springer New York LLC, 2016. lpp. 29-47 (Springer Proceedings in Mathematics and Statistics; Sēj. 180).

Zinātniskās darbības rezultāts: Nodaļa grāmatā/enciklopēdijā/konferences krājumā › Konferences zinātniskais raksts › Pētniecība › koleģiāli recenzēts

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T1 - Periodic solutions of the second order quadratic rational difference equation xn+1 = α/(1+xn)xn-1

AU - Bula, Inese

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2016.

PY - 2016

Y1 - 2016

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.

AB - 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.

KW - Difference equation

KW - Equilibrium point

KW - Periodic solution

KW - Rational difference equation

UR - https://www.scopus.com/pages/publications/84994805528

U2 - 10.1007/978-3-662-52927-0_3

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

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AN - SCOPUS:84994805528

SN - 9783662529263

T3 - Springer Proceedings in Mathematics and Statistics

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EP - 47

BT - Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012

A2 - Cushing, Jim M.

A2 - Pinto, Alberto A.

A2 - Elaydi, Saber

A2 - i Soler, Lluis Alseda

PB - Springer New York LLC

T2 - 18th International Conference on Difference Equations and Applications, ICDEA 2012

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Bula I. Periodic solutions of the second order quadratic rational difference equation x_n+1 = α/(1+x_n)x_n-1. (gadā) Cushing JM, Pinto AA, Elaydi S, i Soler LA, redaktori, Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012. Springer New York LLC. 2016. lpp. 29-47. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-662-52927-0_3