Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation
A method is proposed for calculating the normal form coefficients of the degenerate Hopf bifurcation system and the steady periodic solutions of a nonlinear vibration system. The results obtained by this method are the same as those obtained by the classical one. The present method is much simpler a...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1994-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1994-1303 |
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| _version_ | 1832567386915471360 |
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| author | A.Y.T. Leung Zhang Qichang Chen Yushu |
| author_facet | A.Y.T. Leung Zhang Qichang Chen Yushu |
| author_sort | A.Y.T. Leung |
| collection | DOAJ |
| description | A method is proposed for calculating the normal form coefficients of the degenerate Hopf bifurcation system and the steady periodic solutions of a nonlinear vibration system. The results obtained by this method are the same as those obtained by the classical one. The present method is much simpler and can easily be implemented: that is, given the coefficients of the governing equations, the response is obtained directly by substitution. |
| format | Article |
| id | doaj-art-8f82023cdf4445f090f718a7676d7696 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-8f82023cdf4445f090f718a7676d76962025-02-03T01:01:34ZengWileyShock and Vibration1070-96221875-92031994-01-011323324010.3233/SAV-1994-1303Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s EquationA.Y.T. Leung0Zhang Qichang1Chen Yushu2Department of Civil and Structural Engineering, University of Hong Kong, Hong KongDepartment of Mechanics, Tianjin University, ChinaDepartment of Mechanics, Tianjin University, ChinaA method is proposed for calculating the normal form coefficients of the degenerate Hopf bifurcation system and the steady periodic solutions of a nonlinear vibration system. The results obtained by this method are the same as those obtained by the classical one. The present method is much simpler and can easily be implemented: that is, given the coefficients of the governing equations, the response is obtained directly by substitution.http://dx.doi.org/10.3233/SAV-1994-1303 |
| spellingShingle | A.Y.T. Leung Zhang Qichang Chen Yushu Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation Shock and Vibration |
| title | Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation |
| title_full | Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation |
| title_fullStr | Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation |
| title_full_unstemmed | Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation |
| title_short | Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation |
| title_sort | normal form analysis of hopf bifurcation exemplified by duffing s equation |
| url | http://dx.doi.org/10.3233/SAV-1994-1303 |
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