Dynamics of the rational difference equations
Discrete-time systems are sometimes used to explain natural phenomena that happen in non-linear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations of generalized order in this paper. Using the standard iteration meth...
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| Format: | Article |
| Language: | English |
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Kyrgyz Turkish Manas University
2024-12-01
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| Series: | MANAS: Journal of Engineering |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3664051 |
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| author | Burak Oğul |
| author_facet | Burak Oğul |
| author_sort | Burak Oğul |
| collection | DOAJ |
| description | Discrete-time systems are sometimes used to explain natural phenomena that happen in non-linear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations of generalized order in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work’s validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. nIn this research, we examine the qualitative behavior of rational recursive sequences provided that the initial conditions are arbitrary real numbers. We examine the behavior of solutions on graphs according to the state of their initial valueb 𝑥𝑛+1 = 𝑥𝑛𝑥𝑛−8 ±𝑥𝑛−7 ± 𝑥𝑛𝑥𝑛−7𝑥𝑛−8 , 𝑛 ∈ N0. |
| format | Article |
| id | doaj-art-621c255187da4816ac6ea2b09b086e0a |
| institution | Kabale University |
| issn | 1694-7398 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Kyrgyz Turkish Manas University |
| record_format | Article |
| series | MANAS: Journal of Engineering |
| spelling | doaj-art-621c255187da4816ac6ea2b09b086e0a2025-01-08T09:28:22ZengKyrgyz Turkish Manas UniversityMANAS: Journal of Engineering1694-73982024-12-0112217718410.51354/mjen.14207611437Dynamics of the rational difference equationsBurak Oğul0https://orcid.org/0000-0002-3264-4340ISTANBUL AYDIN UNIVERSITYDiscrete-time systems are sometimes used to explain natural phenomena that happen in non-linear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations of generalized order in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work’s validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. nIn this research, we examine the qualitative behavior of rational recursive sequences provided that the initial conditions are arbitrary real numbers. We examine the behavior of solutions on graphs according to the state of their initial valueb 𝑥𝑛+1 = 𝑥𝑛𝑥𝑛−8 ±𝑥𝑛−7 ± 𝑥𝑛𝑥𝑛−7𝑥𝑛−8 , 𝑛 ∈ N0.https://dergipark.org.tr/en/download/article-file/3664051equilibriumpointsolution of differenceequationstabilityboundednessglobal asymptotic stability*corresponding |
| spellingShingle | Burak Oğul Dynamics of the rational difference equations MANAS: Journal of Engineering equilibriumpoint solution of differenceequation stability boundedness global asymptotic stability*corresponding |
| title | Dynamics of the rational difference equations |
| title_full | Dynamics of the rational difference equations |
| title_fullStr | Dynamics of the rational difference equations |
| title_full_unstemmed | Dynamics of the rational difference equations |
| title_short | Dynamics of the rational difference equations |
| title_sort | dynamics of the rational difference equations |
| topic | equilibriumpoint solution of differenceequation stability boundedness global asymptotic stability*corresponding |
| url | https://dergipark.org.tr/en/download/article-file/3664051 |
| work_keys_str_mv | AT burakogul dynamicsoftherationaldifferenceequations |