Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay
We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifol...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/768364 |
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| _version_ | 1832550048339066880 |
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| author | Xiaojian Zhou Xin Chen Yongzhong Song |
| author_facet | Xiaojian Zhou Xin Chen Yongzhong Song |
| author_sort | Xiaojian Zhou |
| collection | DOAJ |
| description | We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis. |
| format | Article |
| id | doaj-art-1a96198101b4449aafa64c0f245a91d2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1a96198101b4449aafa64c0f245a91d22025-02-03T06:07:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/768364768364Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time DelayXiaojian Zhou0Xin Chen1Yongzhong Song2Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaJiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaJiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaWe investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.http://dx.doi.org/10.1155/2012/768364 |
| spellingShingle | Xiaojian Zhou Xin Chen Yongzhong Song Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay Journal of Applied Mathematics |
| title | Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay |
| title_full | Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay |
| title_fullStr | Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay |
| title_full_unstemmed | Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay |
| title_short | Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay |
| title_sort | hopf bifurcation of a differential algebraic bioeconomic model with time delay |
| url | http://dx.doi.org/10.1155/2012/768364 |
| work_keys_str_mv | AT xiaojianzhou hopfbifurcationofadifferentialalgebraicbioeconomicmodelwithtimedelay AT xinchen hopfbifurcationofadifferentialalgebraicbioeconomicmodelwithtimedelay AT yongzhongsong hopfbifurcationofadifferentialalgebraicbioeconomicmodelwithtimedelay |