Unusual Nonpolynomial Van der Pol Oscillator Equations With Exact Harmonic and Isochronous Solutions

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AuteurADJAI, K K DAMIEN
AuteurNONTI, MARCELLIN
AuteurAKANDE, JEAN
AuteurMONSIA, MARC DELPHIN
Date d'ajout2026-06-02T16:06:57Z
Date de disponibilite2026-06-02T16:06:57Z
Date de publication2022
ResumeWe do not know Van der Pol-type equations with nonlinear restoring force having explicitly an exact periodic solution. We present, for the first time, nonpolynomial Van der Pol oscillator equations that do not satisfy the classical existence theorems. We exhibit their exact harmonic and isochronous solutions and prove the existence of limit cycles by using averaging theory. We also present first integrals and exact solutions of polynomial Van der Pol-Duffing equations to show that they do not have any limit cycle. Additionally, we prove that the damped Duffing-type equations are equivalent to the conservative Duffing equations exhibiting nonoscillatory solutions.
Autre identifiantBECDB-13324
URIhttps://dspace.uac.bj/handle/123456789/11433
Languefr
Fait partie deInt. J. Anal. Appl.
SujetVan der Pol-Duffing equation
Sujetnonpolynomial Van der Pol-type oscillator
Sujetdamped Duffing
Sujetequation
Sujetfirst integrals
Sujetexact harmonic and limit cycle solutions
Sujetexistence theorem
TitreUnusual Nonpolynomial Van der Pol Oscillator Equations With Exact Harmonic and Isochronous Solutions
TypeArticle

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