On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations

Nabil Sellami, Romaissa Mellal, Bahri Belkacem Cherif, Sahar Ahmed Idris and Sundarapandian Vaidyanathan

Discrete Dynamics in Nature and Society, 2021, vol. 2021, 1-18

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:6996805

DOI: 10.1155/2021/6996805

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