Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays
A coupled system of nine identical cells with delays and 𝔻3×𝔻3-symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability o...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/417678 |
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| author | Haijun Hu Li Liu Jie Mao |
| author_facet | Haijun Hu Li Liu Jie Mao |
| author_sort | Haijun Hu |
| collection | DOAJ |
| description | A coupled system of nine identical cells with delays and 𝔻3×𝔻3-symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the
bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results. |
| format | Article |
| id | doaj-art-5ecd4d4d95b74b52b447b616e6bd57e1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5ecd4d4d95b74b52b447b616e6bd57e12025-02-03T01:21:23ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/417678417678Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with DelaysHaijun Hu0Li Liu1Jie Mao2College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, ChinaCollege of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, ChinaCollege of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, ChinaA coupled system of nine identical cells with delays and 𝔻3×𝔻3-symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results.http://dx.doi.org/10.1155/2013/417678 |
| spellingShingle | Haijun Hu Li Liu Jie Mao Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays Abstract and Applied Analysis |
| title | Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays |
| title_full | Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays |
| title_fullStr | Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays |
| title_full_unstemmed | Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays |
| title_short | Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays |
| title_sort | multiple nonlinear oscillations in a 𝔻3 𝔻3 symmetrical coupled system of identical cells with delays |
| url | http://dx.doi.org/10.1155/2013/417678 |
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