Dynamics and Expression of Solution of a Sixth Order Difference Equation
This paper deals with the solution behavior and periodic nature of the solutions of the difference equation $$ s_{n+1}=\alpha s_{n}+\dfrac{\beta s_{n}s_{n-4}}{\gamma s_{n-4}+\delta s_{n-5} },\;\;\;n=0,1,... $$ {\Large \noindent }where the initial conditions $s_{-5},\ s_{-4},\ s_{-3},\ s_{-2},\ s_{-1...
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| Format: | Article |
| Language: | English |
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Mahmut Akyigit
2021-08-01
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| Series: | Journal of Mathematical Sciences and Modelling |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/1740910 |
| Summary: | This paper deals with the solution behavior and periodic nature of the solutions of the difference equation $$ s_{n+1}=\alpha s_{n}+\dfrac{\beta s_{n}s_{n-4}}{\gamma s_{n-4}+\delta s_{n-5} },\;\;\;n=0,1,... $$ {\Large \noindent }where the initial conditions $s_{-5},\ s_{-4},\ s_{-3},\ s_{-2},\ s_{-1},\ s_{0}$ are arbitrary positive real numbers and $\alpha ,\ \beta ,\ \gamma ,\ \delta \ $are positive constants. Also we obtain the closed form of the solutions of some special cases of this equation. |
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| ISSN: | 2636-8692 |