Year 2020, Volume 8 , Issue 1, Pages 68 - 76 2020-06-30

Stability of the third order rational difference equation

Mehmet Emre ERDOĞAN [1]


In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\] where the initial conditions are non zero real numbers and are positive constants such that \[\alpha+\beta\leq \gamma+\theta.\] Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.
Asymptotic Stability, Difference Equation, Global Behavior
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Primary Language en
Subjects Engineering
Journal Section Research Article
Authors

Orcid: 0000-0002-7421-0815
Author: Mehmet Emre ERDOĞAN (Primary Author)
Institution: SELCUK UNIVERSITY
Country: Turkey


Dates

Publication Date : June 30, 2020

Bibtex @research article { mjen713656, journal = {MANAS Journal of Engineering}, issn = {1694-7398}, eissn = {1694-7398}, address = {}, publisher = {Kyrgyz-Turkish Manas University}, year = {2020}, volume = {8}, pages = {68 - 76}, doi = {}, title = {Stability of the third order rational difference equation}, key = {cite}, author = {Erdoğan, Mehmet Emre} }
APA Erdoğan, M . (2020). Stability of the third order rational difference equation. MANAS Journal of Engineering , 8 (1) , 68-76 . Retrieved from https://dergipark.org.tr/en/pub/mjen/issue/55261/713656
MLA Erdoğan, M . "Stability of the third order rational difference equation". MANAS Journal of Engineering 8 (2020 ): 68-76 <https://dergipark.org.tr/en/pub/mjen/issue/55261/713656>
Chicago Erdoğan, M . "Stability of the third order rational difference equation". MANAS Journal of Engineering 8 (2020 ): 68-76
RIS TY - JOUR T1 - Stability of the third order rational difference equation AU - Mehmet Emre Erdoğan Y1 - 2020 PY - 2020 N1 - DO - T2 - MANAS Journal of Engineering JF - Journal JO - JOR SP - 68 EP - 76 VL - 8 IS - 1 SN - 1694-7398-1694-7398 M3 - UR - Y2 - 2020 ER -
EndNote %0 MANAS Journal of Engineering Stability of the third order rational difference equation %A Mehmet Emre Erdoğan %T Stability of the third order rational difference equation %D 2020 %J MANAS Journal of Engineering %P 1694-7398-1694-7398 %V 8 %N 1 %R %U
ISNAD Erdoğan, Mehmet Emre . "Stability of the third order rational difference equation". MANAS Journal of Engineering 8 / 1 (June 2020): 68-76 .
AMA Erdoğan M . Stability of the third order rational difference equation. MJEN. 2020; 8(1): 68-76.
Vancouver Erdoğan M . Stability of the third order rational difference equation. MANAS Journal of Engineering. 2020; 8(1): 76-68.