Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$
The main goal of this paper is to study the bifurcation of a second order rational difference equation $$x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+Cx_{n-1}}, ~~n=0, 1, 2, \ldots$$ with positive parameters $\alpha, \beta, A, B, C$ and non-negative initial conditions $\{x_{-k}, x_{-k+1}, \ldots, x_...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2022-06-01
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| Series: | Communications in Advanced Mathematical Sciences |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2098562 |
| _version_ | 1797294222174322688 |
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| author | Batool Raddad Mohammad Saleh |
| author_facet | Batool Raddad Mohammad Saleh |
| author_sort | Batool Raddad |
| collection | DOAJ |
| description | The main goal of this paper is to study the bifurcation of a second order rational difference equation
$$x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+Cx_{n-1}}, ~~n=0, 1, 2, \ldots$$
with positive parameters $\alpha, \beta, A, B, C$ and non-negative initial conditions $\{x_{-k}, x_{-k+1}, \ldots, x_{0}\}$. We study the dynamic behavior and the direction of the bifurcation of the period-two cycle. Numerical discussion with figures are given to support our results. |
| first_indexed | 2024-03-07T21:27:06Z |
| format | Article |
| id | doaj.art-a2c756342e4348369c12131af623b4d8 |
| institution | Directory Open Access Journal |
| issn | 2651-4001 |
| language | English |
| last_indexed | 2024-03-07T21:27:06Z |
| publishDate | 2022-06-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj.art-a2c756342e4348369c12131af623b4d82024-02-27T04:36:36ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012022-06-0152788710.33434/cams.10281221225Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$Batool Raddad0Mohammad Saleh1Birzeit UniversityBirzeit UniversityThe main goal of this paper is to study the bifurcation of a second order rational difference equation $$x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+Cx_{n-1}}, ~~n=0, 1, 2, \ldots$$ with positive parameters $\alpha, \beta, A, B, C$ and non-negative initial conditions $\{x_{-k}, x_{-k+1}, \ldots, x_{0}\}$. We study the dynamic behavior and the direction of the bifurcation of the period-two cycle. Numerical discussion with figures are given to support our results.https://dergipark.org.tr/tr/download/article-file/2098562stabilitybifurcationchaos |
| spellingShingle | Batool Raddad Mohammad Saleh Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$ Communications in Advanced Mathematical Sciences stability bifurcation chaos |
| title | Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$ |
| title_full | Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$ |
| title_fullStr | Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$ |
| title_full_unstemmed | Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$ |
| title_short | Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$ |
| title_sort | dynamics and bifurcation of x n 1 frac alpha beta x n 1 a bx n c x n 1 |
| topic | stability bifurcation chaos |
| url | https://dergipark.org.tr/tr/download/article-file/2098562 |
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