Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback
The dynamics of a kind of electromechanical coupling deformable micromirror device torsion micromirror with delay are investigated. Based on the distribution of eigenvalues, we prove that a sequence of Hopf bifurcation occurs at the equilibrium as the delay increases and obtain the critical values o...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/752539 |
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| _version_ | 1832548709787762688 |
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| author | Yanqiu Li Wei Duan Shujian Ma Pengfei Li |
| author_facet | Yanqiu Li Wei Duan Shujian Ma Pengfei Li |
| author_sort | Yanqiu Li |
| collection | DOAJ |
| description | The dynamics of a kind of electromechanical coupling deformable micromirror
device torsion micromirror with delay are investigated. Based on the distribution
of eigenvalues, we prove that a sequence of Hopf bifurcation occurs at the equilibrium as the delay increases and obtain the critical values of Hopf bifurcation.
Explicit algorithms for determining the direction of the Hopf bifurcation and the
stability of the bifurcating periodic solutions are derived, using the theories of
normal form and center manifold. |
| format | Article |
| id | doaj-art-dfd85b91c9614580902aae9d9d4a129c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-dfd85b91c9614580902aae9d9d4a129c2025-02-03T06:13:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/752539752539Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay FeedbackYanqiu Li0Wei Duan1Shujian Ma2Pengfei Li3Department of Applied Mathematics, Nanjing University of Technology, Nanjing 211816, ChinaPetro-China West-East Gas Pipeline Company, Yangzhou 225009, ChinaDepartment of Applied Mathematics, Nanjing University of Technology, Nanjing 211816, ChinaDepartment of Applied Mathematics, Nanjing University of Technology, Nanjing 211816, ChinaThe dynamics of a kind of electromechanical coupling deformable micromirror device torsion micromirror with delay are investigated. Based on the distribution of eigenvalues, we prove that a sequence of Hopf bifurcation occurs at the equilibrium as the delay increases and obtain the critical values of Hopf bifurcation. Explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived, using the theories of normal form and center manifold.http://dx.doi.org/10.1155/2014/752539 |
| spellingShingle | Yanqiu Li Wei Duan Shujian Ma Pengfei Li Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback Journal of Applied Mathematics |
| title | Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback |
| title_full | Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback |
| title_fullStr | Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback |
| title_full_unstemmed | Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback |
| title_short | Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback |
| title_sort | bifurcation of a microelectromechanical nonlinear coupling system with delay feedback |
| url | http://dx.doi.org/10.1155/2014/752539 |
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