On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation
The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. Visual example...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/5726617 |
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| _version_ | 1832545257950019584 |
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| author | M. E. Erdogan |
| author_facet | M. E. Erdogan |
| author_sort | M. E. Erdogan |
| collection | DOAJ |
| description | The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB. |
| format | Article |
| id | doaj-art-b4c3e9bc14bc47b1994b08b4eca2e523 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b4c3e9bc14bc47b1994b08b4eca2e5232025-02-03T07:26:21ZengWileyJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/5726617On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference EquationM. E. Erdogan0Department of MathematicsThe main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB.http://dx.doi.org/10.1155/2023/5726617 |
| spellingShingle | M. E. Erdogan On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation Journal of Applied Mathematics |
| title | On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation |
| title_full | On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation |
| title_fullStr | On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation |
| title_full_unstemmed | On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation |
| title_short | On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation |
| title_sort | on the global asymptotic stability and 4 period oscillation of the third order difference equation |
| url | http://dx.doi.org/10.1155/2023/5726617 |
| work_keys_str_mv | AT meerdogan ontheglobalasymptoticstabilityand4periodoscillationofthethirdorderdifferenceequation |