About a System of Piecewise Linear Difference Equations with Many Periodic Solutions

Inese Bula; Agnese Sīle

doi:10.1007/978-3-031-51049-6_2

About a System of Piecewise Linear Difference Equations with Many Periodic Solutions

Inese Bula^*
, Agnese Sīle

^*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

We want to draw attention to the system of first order piecewise linear difference equations of two equations (formula presented), where the parameters b and d are any positive real numbers. We will show that this system has interesting behavior compared to other similar systems. We show that there exists an unstable equilibrium (d,-b). It has been shown that there are no solutions with period 2 and 3, but depending on the values of parameters b and d there are solutions with periods 5, 6, 7, 11, 12, 13, 16, 17, 18, 19, 20, 24, 25, 27, 30, 36. We have a hypothesis that all solutions are eventually periodic solutions.

Oriģinālvaloda	Angļu
Rīkotāja publikācijas nosaukums	Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022
Redaktori	Sorin Olaru, Jim Cushing, Saber Elaydi, René Lozi
Izdevējs	Springer
Lapas	29-50
Lapu skaits	22
ISBN (Drukātā versija)	9783031510489
DOIs	https://doi.org/10.1007/978-3-031-51049-6_2
Publikācijas statuss	Publicēts - 2024
Pasākums	27th International Conference on Difference Equations and Applications, ICDEA 2022 - Paris-Saclay, Francija Ilgums: 18 jūn. 2022 → 22 jūn. 2022

Publikāciju sērijas

Nosaukums	Springer Proceedings in Mathematics and Statistics
Sējums	444
ISSN (Drukātā versija)	2194-1009
ISSN (Elektroniskā versija)	2194-1017

Konference

Konference	27th International Conference on Difference Equations and Applications, ICDEA 2022
Valsts/Teritorija	Francija
Pilsēta	Paris-Saclay
Periods	18/06/22 → 22/06/22

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10.1007/978-3-031-51049-6_2

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Bula, I., & Sīle, A. (2024). About a System of Piecewise Linear Difference Equations with Many Periodic Solutions. (gadā) S. Olaru, J. Cushing, S. Elaydi, & R. Lozi (Red.), Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022 (lpp. 29-50). (Springer Proceedings in Mathematics and Statistics; Sēj. 444). Springer. https://doi.org/10.1007/978-3-031-51049-6_2

@inproceedings{75e3c08a3d1f495b9b0fc9a896ad2111,

title = "About a System of Piecewise Linear Difference Equations with Many Periodic Solutions",

abstract = "We want to draw attention to the system of first order piecewise linear difference equations of two equations (formula presented), where the parameters b and d are any positive real numbers. We will show that this system has interesting behavior compared to other similar systems. We show that there exists an unstable equilibrium (d,-b). It has been shown that there are no solutions with period 2 and 3, but depending on the values of parameters b and d there are solutions with periods 5, 6, 7, 11, 12, 13, 16, 17, 18, 19, 20, 24, 25, 27, 30, 36. We have a hypothesis that all solutions are eventually periodic solutions.",

keywords = "Equilibrium, Eventually periodic solution, Periodic solution, Stability, System of difference equations",

author = "Inese Bula and Agnese Sīle",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 27th International Conference on Difference Equations and Applications, ICDEA 2022 ; Conference date: 18-06-2022 Through 22-06-2022",

year = "2024",

doi = "10.1007/978-3-031-51049-6\_2",

language = "English",

isbn = "9783031510489",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "29--50",

editor = "Sorin Olaru and Jim Cushing and Saber Elaydi and Ren{\'e} Lozi",

booktitle = "Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022",

address = "Germany",

}

Bula, I & Sīle, A 2024, About a System of Piecewise Linear Difference Equations with Many Periodic Solutions. (kur) S Olaru, J Cushing, S Elaydi & R Lozi (red.), Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022. Springer Proceedings in Mathematics and Statistics, sēj. 444, Springer, lpp. 29-50, 27th International Conference on Difference Equations and Applications, ICDEA 2022, Paris-Saclay, Francija, 18/06/22. https://doi.org/10.1007/978-3-031-51049-6_2

About a System of Piecewise Linear Difference Equations with Many Periodic Solutions. / Bula, Inese; Sīle, Agnese.
Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022. red. / Sorin Olaru; Jim Cushing; Saber Elaydi; René Lozi. Springer, 2024. lpp. 29-50 (Springer Proceedings in Mathematics and Statistics; Sēj. 444).

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

TY - GEN

T1 - About a System of Piecewise Linear Difference Equations with Many Periodic Solutions

AU - Bula, Inese

AU - Sīle, Agnese

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - We want to draw attention to the system of first order piecewise linear difference equations of two equations (formula presented), where the parameters b and d are any positive real numbers. We will show that this system has interesting behavior compared to other similar systems. We show that there exists an unstable equilibrium (d,-b). It has been shown that there are no solutions with period 2 and 3, but depending on the values of parameters b and d there are solutions with periods 5, 6, 7, 11, 12, 13, 16, 17, 18, 19, 20, 24, 25, 27, 30, 36. We have a hypothesis that all solutions are eventually periodic solutions.

AB - We want to draw attention to the system of first order piecewise linear difference equations of two equations (formula presented), where the parameters b and d are any positive real numbers. We will show that this system has interesting behavior compared to other similar systems. We show that there exists an unstable equilibrium (d,-b). It has been shown that there are no solutions with period 2 and 3, but depending on the values of parameters b and d there are solutions with periods 5, 6, 7, 11, 12, 13, 16, 17, 18, 19, 20, 24, 25, 27, 30, 36. We have a hypothesis that all solutions are eventually periodic solutions.

KW - Equilibrium

KW - Eventually periodic solution

KW - Periodic solution

KW - Stability

KW - System of difference equations

UR - https://www.scopus.com/pages/publications/85187639159

U2 - 10.1007/978-3-031-51049-6_2

DO - 10.1007/978-3-031-51049-6_2

M3 - Conference paper

AN - SCOPUS:85187639159

SN - 9783031510489

T3 - Springer Proceedings in Mathematics and Statistics

SP - 29

EP - 50

BT - Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022

A2 - Olaru, Sorin

A2 - Cushing, Jim

A2 - Elaydi, Saber

A2 - Lozi, René

PB - Springer

T2 - 27th International Conference on Difference Equations and Applications, ICDEA 2022

Y2 - 18 June 2022 through 22 June 2022

ER -

About a System of Piecewise Linear Difference Equations with Many Periodic Solutions

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