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Article: An algorithm for higher order Hopf normal forms

TitleAn algorithm for higher order Hopf normal forms
Authors
Issue Date1995
PublisherHindawi Publishing Corporation. The Journal's web site is located at http://www.hindawi.com/journals/sv/
Citation
Shock and Vibration, 1995, v. 2 n. 4, p. 307-319 How to Cite?
AbstractNormal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.
Persistent Identifierhttp://hdl.handle.net/10722/211399
ISSN
2015 Impact Factor: 0.88
2015 SCImago Journal Rankings: 0.406

 

DC FieldValueLanguage
dc.contributor.authorLeung, AYT-
dc.contributor.authorGe, T-
dc.date.accessioned2015-07-10T07:24:49Z-
dc.date.available2015-07-10T07:24:49Z-
dc.date.issued1995-
dc.identifier.citationShock and Vibration, 1995, v. 2 n. 4, p. 307-319-
dc.identifier.issn1070-9622-
dc.identifier.urihttp://hdl.handle.net/10722/211399-
dc.description.abstractNormal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.-
dc.languageeng-
dc.publisherHindawi Publishing Corporation. The Journal's web site is located at http://www.hindawi.com/journals/sv/-
dc.relation.ispartofShock and Vibration-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleAn algorithm for higher order Hopf normal forms-
dc.typeArticle-
dc.identifier.emailLeung, AYT: ytleung@hkucc.hku.hk-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.3233/SAV-1995-2405-
dc.identifier.hkuros5709-
dc.identifier.hkuros8717-
dc.identifier.volume2-
dc.identifier.issue4-
dc.identifier.spage307-
dc.identifier.epage319-
dc.publisher.placeNetherlands-

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