On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations
We study the limit cycles of the fifth-order differential equation x⋅⋅⋅⋅⋅−ex⃜−dx⃛−cx¨−bx˙−ax=εFx,x˙,x¨,x⋯,x⃜ with a=λμδ,b=−λμ+λδ+μδ,c=λ+μ+δ+λμδ,d=−1+λμ+λδ+μδ,e=λ+μ+δ, where ε is a small enough real parameter, λ,μ, and δ are real parameters, and F∈C2 is a nonlinear function. Using the averaging theor...
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| Main Authors: | , , , |
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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/10.1155/2021/6996805 |
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| author | Nabil Sellami Romaissa Mellal Bahri Belkacem Cherif Sahar Ahmed Idris |
| author_facet | Nabil Sellami Romaissa Mellal Bahri Belkacem Cherif Sahar Ahmed Idris |
| author_sort | Nabil Sellami |
| collection | DOAJ |
| description | We study the limit cycles of the fifth-order differential equation x⋅⋅⋅⋅⋅−ex⃜−dx⃛−cx¨−bx˙−ax=εFx,x˙,x¨,x⋯,x⃜ with a=λμδ,b=−λμ+λδ+μδ,c=λ+μ+δ+λμδ,d=−1+λμ+λδ+μδ,e=λ+μ+δ, where ε is a small enough real parameter, λ,μ, and δ are real parameters, and F∈C2 is a nonlinear function. Using the averaging theory of first order, we provide sufficient conditions for the existence of limit cycles of this equation. |
| format | Article |
| id | doaj-art-17bc382e13944e599b4a485840df98ea |
| 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-17bc382e13944e599b4a485840df98ea2025-02-03T01:26:55ZengWileyDiscrete Dynamics in Nature and Society1607-887X2021-01-01202110.1155/2021/6996805On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential EquationsNabil Sellami0Romaissa Mellal1Bahri Belkacem Cherif2Sahar Ahmed Idris3Department of MathematicsDepartment of MathematicsDepartment of MathematicsCollege of Industrial EngineeringWe study the limit cycles of the fifth-order differential equation x⋅⋅⋅⋅⋅−ex⃜−dx⃛−cx¨−bx˙−ax=εFx,x˙,x¨,x⋯,x⃜ with a=λμδ,b=−λμ+λδ+μδ,c=λ+μ+δ+λμδ,d=−1+λμ+λδ+μδ,e=λ+μ+δ, where ε is a small enough real parameter, λ,μ, and δ are real parameters, and F∈C2 is a nonlinear function. Using the averaging theory of first order, we provide sufficient conditions for the existence of limit cycles of this equation.http://dx.doi.org/10.1155/2021/6996805 |
| spellingShingle | Nabil Sellami Romaissa Mellal Bahri Belkacem Cherif Sahar Ahmed Idris On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations Discrete Dynamics in Nature and Society |
| title | On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations |
| title_full | On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations |
| title_fullStr | On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations |
| title_full_unstemmed | On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations |
| title_short | On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations |
| title_sort | on the limit cycles for a class of perturbed fifth order autonomous differential equations |
| url | http://dx.doi.org/10.1155/2021/6996805 |
| work_keys_str_mv | AT nabilsellami onthelimitcyclesforaclassofperturbedfifthorderautonomousdifferentialequations AT romaissamellal onthelimitcyclesforaclassofperturbedfifthorderautonomousdifferentialequations AT bahribelkacemcherif onthelimitcyclesforaclassofperturbedfifthorderautonomousdifferentialequations AT saharahmedidris onthelimitcyclesforaclassofperturbedfifthorderautonomousdifferentialequations |