Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations
In this work, we derive the solution formulas and study their behaviors for the difference equations xn+1=αxnxn−3/−βxn−3+γxn−2,n∈ℕ0 and xn+1=αxnxn−3/βxn−3−γxn−2,n∈ℕ0 with real initials and positive parameters. We show that there exist periodic solutions for the second equation under certain conditio...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6622538 |
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| author | Raafat Abo-Zeid Abdul Qadeer Khan |
| author_facet | Raafat Abo-Zeid Abdul Qadeer Khan |
| author_sort | Raafat Abo-Zeid |
| collection | DOAJ |
| description | In this work, we derive the solution formulas and study their behaviors for the difference equations xn+1=αxnxn−3/−βxn−3+γxn−2,n∈ℕ0 and xn+1=αxnxn−3/βxn−3−γxn−2,n∈ℕ0 with real initials and positive parameters. We show that there exist periodic solutions for the second equation under certain conditions when β2<4αγ. Finally, we give some illustrative examples. |
| format | Article |
| id | doaj-art-ae8da44c3bae4bcb9ebfbb129f1b4f7d |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ae8da44c3bae4bcb9ebfbb129f1b4f7d2025-02-03T01:33:21ZengWileyDiscrete Dynamics in Nature and Society1607-887X2021-01-01202110.1155/2021/6622538Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference EquationsRaafat Abo-Zeid0Abdul Qadeer Khan1Department of Basic ScienceDepartment of MathematicsIn this work, we derive the solution formulas and study their behaviors for the difference equations xn+1=αxnxn−3/−βxn−3+γxn−2,n∈ℕ0 and xn+1=αxnxn−3/βxn−3−γxn−2,n∈ℕ0 with real initials and positive parameters. We show that there exist periodic solutions for the second equation under certain conditions when β2<4αγ. Finally, we give some illustrative examples.http://dx.doi.org/10.1155/2021/6622538 |
| spellingShingle | Raafat Abo-Zeid Abdul Qadeer Khan Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations Discrete Dynamics in Nature and Society |
| title | Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations |
| title_full | Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations |
| title_fullStr | Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations |
| title_full_unstemmed | Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations |
| title_short | Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations |
| title_sort | behaviors of the solutions via their closed form formulas for two rational third order difference equations |
| url | http://dx.doi.org/10.1155/2021/6622538 |
| work_keys_str_mv | AT raafatabozeid behaviorsofthesolutionsviatheirclosedformformulasfortworationalthirdorderdifferenceequations AT abdulqadeerkhan behaviorsofthesolutionsviatheirclosedformformulasfortworationalthirdorderdifferenceequations |