Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays
In this paper, a Lengyel–Epstein model with two delays is proposed and considered. By choosing the different delay as a parameter, the stability and Hopf bifurcation of the system under different situations are investigated in detail by using the linear stability method. Furthermore, the sufficient...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5554562 |
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| author | Long Li Yanxia Zhang |
| author_facet | Long Li Yanxia Zhang |
| author_sort | Long Li |
| collection | DOAJ |
| description | In this paper, a Lengyel–Epstein model with two delays is proposed and considered. By choosing the different delay as a parameter, the stability and Hopf bifurcation of the system under different situations are investigated in detail by using the linear stability method. Furthermore, the sufficient conditions for the stability of the equilibrium and the Hopf conditions are obtained. In addition, the explicit formula determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained with the normal form theory and the center manifold theorem to delay differential equations. Some numerical examples and simulation results are also conducted at the end of this paper to validate the developed theories. |
| format | Article |
| id | doaj-art-313c9216fcf04b69b3e1c85c76b6e419 |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-313c9216fcf04b69b3e1c85c76b6e4192025-08-20T02:38:55ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55545625554562Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two DelaysLong Li0Yanxia Zhang1School of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, ChinaSchool of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, ChinaIn this paper, a Lengyel–Epstein model with two delays is proposed and considered. By choosing the different delay as a parameter, the stability and Hopf bifurcation of the system under different situations are investigated in detail by using the linear stability method. Furthermore, the sufficient conditions for the stability of the equilibrium and the Hopf conditions are obtained. In addition, the explicit formula determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained with the normal form theory and the center manifold theorem to delay differential equations. Some numerical examples and simulation results are also conducted at the end of this paper to validate the developed theories.http://dx.doi.org/10.1155/2021/5554562 |
| spellingShingle | Long Li Yanxia Zhang Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays Journal of Mathematics |
| title | Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays |
| title_full | Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays |
| title_fullStr | Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays |
| title_full_unstemmed | Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays |
| title_short | Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays |
| title_sort | dynamic analysis and hopf bifurcation of a lengyel epstein system with two delays |
| url | http://dx.doi.org/10.1155/2021/5554562 |
| work_keys_str_mv | AT longli dynamicanalysisandhopfbifurcationofalengyelepsteinsystemwithtwodelays AT yanxiazhang dynamicanalysisandhopfbifurcationofalengyelepsteinsystemwithtwodelays |