Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays
A class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or th...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/958140 |
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| _version_ | 1849413183447498752 |
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| author | Xin-You Meng Hai-Feng Huo |
| author_facet | Xin-You Meng Hai-Feng Huo |
| author_sort | Xin-You Meng |
| collection | DOAJ |
| description | A class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998). Numerical simulations are given to support the theoretical results. |
| format | Article |
| id | doaj-art-5a24f6c7d8a84c1e903cbea3133eb14d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5a24f6c7d8a84c1e903cbea3133eb14d2025-08-20T03:34:12ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/958140958140Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple DelaysXin-You Meng0Hai-Feng Huo1School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaA class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998). Numerical simulations are given to support the theoretical results.http://dx.doi.org/10.1155/2014/958140 |
| spellingShingle | Xin-You Meng Hai-Feng Huo Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays Abstract and Applied Analysis |
| title | Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays |
| title_full | Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays |
| title_fullStr | Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays |
| title_full_unstemmed | Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays |
| title_short | Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays |
| title_sort | bifurcation analysis of a lotka volterra mutualistic system with multiple delays |
| url | http://dx.doi.org/10.1155/2014/958140 |
| work_keys_str_mv | AT xinyoumeng bifurcationanalysisofalotkavolterramutualisticsystemwithmultipledelays AT haifenghuo bifurcationanalysisofalotkavolterramutualisticsystemwithmultipledelays |