Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System
The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosing τ as bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/139375 |
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| _version_ | 1841524433408229376 |
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| author | Qingsong Liu Yiping Lin Jingnan Cao Jinde Cao |
| author_facet | Qingsong Liu Yiping Lin Jingnan Cao Jinde Cao |
| author_sort | Qingsong Liu |
| collection | DOAJ |
| description | The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosing τ as bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining
the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the
chaotic behaviors are observed. |
| format | Article |
| id | doaj-art-144b3559eb09423695def7edaf40c5fb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-144b3559eb09423695def7edaf40c5fb2025-02-03T05:53:04ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/139375139375Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein SystemQingsong Liu0Yiping Lin1Jingnan Cao2Jinde Cao3Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, ChinaDepartment of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, ChinaSchool of Computer Science, Beijing University of Post Telecommunication, Beijing 100876, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaThe local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosing τ as bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.http://dx.doi.org/10.1155/2014/139375 |
| spellingShingle | Qingsong Liu Yiping Lin Jingnan Cao Jinde Cao Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System Discrete Dynamics in Nature and Society |
| title | Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System |
| title_full | Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System |
| title_fullStr | Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System |
| title_full_unstemmed | Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System |
| title_short | Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System |
| title_sort | chaos and hopf bifurcation analysis of the delayed local lengyel epstein system |
| url | http://dx.doi.org/10.1155/2014/139375 |
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