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

^*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

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.

Original language	English
Title of host publication	Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022
Editors	Sorin Olaru, Jim Cushing, Saber Elaydi, René Lozi
Publisher	Springer
Pages	29-50
Number of pages	22
ISBN (Print)	9783031510489
DOIs	https://doi.org/10.1007/978-3-031-51049-6_2
Publication status	Published - 2024
Event	27th International Conference on Difference Equations and Applications, ICDEA 2022 - Paris-Saclay, France Duration: 18 Jun 2022 → 22 Jun 2022

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	444
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	27th International Conference on Difference Equations and Applications, ICDEA 2022
Country/Territory	France
City	Paris-Saclay
Period	18/06/22 → 22/06/22

Keywords

Equilibrium
Eventually periodic solution
Periodic solution
Stability
System of difference equations

Access to Document

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

Cite this

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

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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",

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series = "Springer Proceedings in Mathematics and Statistics",

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

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Bula, I & Sīle, A 2024, About a System of Piecewise Linear Difference Equations with Many Periodic Solutions. in S Olaru, J Cushing, S Elaydi & R Lozi (eds), Difference Equations, Discrete Dynamical Systems and Applications - IDCEA 2022. Springer Proceedings in Mathematics and Statistics, vol. 444, Springer, pp. 29-50, 27th International Conference on Difference Equations and Applications, ICDEA 2022, Paris-Saclay, France, 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. ed. / Sorin Olaru; Jim Cushing; Saber Elaydi; René Lozi. Springer, 2024. p. 29-50 (Springer Proceedings in Mathematics and Statistics; Vol. 444).

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

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

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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

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PB - Springer

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

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ER -

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

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