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Journal of Applied Mathematics and Computing

Erschienen in:

11.01.2017 | Original Research

Well-defined solutions of a system of difference equations

verfasst von: Nabila Haddad, Nouressadat Touafek, Julius Fergy T. Rabago

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2018

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Abstract

This note deals with the solution form of the system of difference equations

$$\begin{aligned} x_{n+1}=\frac{a x_{n}y_{n-1}}{y_{n}-\alpha }+\beta ,\quad y_{n+1}=\frac{b x_{n-1}y_{n}}{x_{n}-\beta }+\alpha ,\quad n \in {\mathbb {N}}_{0}, \end{aligned}$$

where the parameters $a,\,b,\,\alpha ,\,\beta $ and initial values $x_{-i},\,y_{-i},\,i=0,1$, are non-zero real numbers. The special case $a=b$ is treated separately, and the qualitative behavior of its solutions is examined. Also, conditions are determined so that the system admits periodic solutions. Finally, numerical examples are provided to support the theoretical results exhibited in the paper.

Vorheriger Artikel Two proximal splitting methods for multi-block separable programming with applications to stable principal component pursuit

Nächster Artikel The G-Euler process for nonlinear autonomous systems

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Titel: Well-defined solutions of a system of difference equations
verfasst von: Nabila Haddad
Nouressadat Touafek
Julius Fergy T. Rabago
Publikationsdatum: 11.01.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2018
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-017-1081-8

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