Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation
A kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/235038 |
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| _version_ | 1841524848817340416 |
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| author | Xiaoqian Cui Junjie Wei |
| author_facet | Xiaoqian Cui Junjie Wei |
| author_sort | Xiaoqian Cui |
| collection | DOAJ |
| description | A kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the
normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results. |
| format | Article |
| id | doaj-art-4528c998b4224b91acbe76f05539785d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4528c998b4224b91acbe76f05539785d2025-02-03T05:47:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/235038235038Bifurcation Analysis in a Kind of Fourth-Order Delay Differential EquationXiaoqian Cui0Junjie Wei1Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, ChinaA kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.http://dx.doi.org/10.1155/2009/235038 |
| spellingShingle | Xiaoqian Cui Junjie Wei Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation Discrete Dynamics in Nature and Society |
| title | Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation |
| title_full | Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation |
| title_fullStr | Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation |
| title_full_unstemmed | Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation |
| title_short | Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation |
| title_sort | bifurcation analysis in a kind of fourth order delay differential equation |
| url | http://dx.doi.org/10.1155/2009/235038 |
| work_keys_str_mv | AT xiaoqiancui bifurcationanalysisinakindoffourthorderdelaydifferentialequation AT junjiewei bifurcationanalysisinakindoffourthorderdelaydifferentialequation |