Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand
This paper is concerned with a delayed model of mutual interactions between the economically active population and the economic growth. The main purpose is to investigate the direction and stability of the bifurcating branch resulting from the increase of delay. By using a second order approximation...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2019/7609828 |
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| _version_ | 1832551717907988480 |
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| author | Sanaa ElFadily Abdelilah Kaddar Khalid Najib |
| author_facet | Sanaa ElFadily Abdelilah Kaddar Khalid Najib |
| author_sort | Sanaa ElFadily |
| collection | DOAJ |
| description | This paper is concerned with a delayed model of mutual interactions between the economically active population and the economic growth. The main purpose is to investigate the direction and stability of the bifurcating branch resulting from the increase of delay. By using a second order approximation of the center manifold, we compute the first Lyapunov coefficient for Hopf bifurcation points and we show that the system under consideration can undergo a supercritical or subcritical Hopf bifurcation and the bifurcating periodic solution is stable or unstable in a neighborhood of some bifurcation points, depending on the choice of parameters. |
| format | Article |
| id | doaj-art-0e2edd8122db4f819eb873eef8791cf8 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-0e2edd8122db4f819eb873eef8791cf82025-02-03T06:00:34ZengWileyInternational Journal of Differential Equations1687-96431687-96512019-01-01201910.1155/2019/76098287609828Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor DemandSanaa ElFadily0Abdelilah Kaddar1Khalid Najib2Mohammadia School of Engineering, Mohammed V University in Rabat, Rabat, MoroccoLaboratoire de Finance, Entrepreneuriat, et Développement, Faculté des Sciences Juridiques, Economiques et Sociales de Salé, Université Mohammed V de Rabat, Sala Al Jadida, MoroccoDepartment of Applied Mathematics, National School of Mineral Industry, Rabat, MoroccoThis paper is concerned with a delayed model of mutual interactions between the economically active population and the economic growth. The main purpose is to investigate the direction and stability of the bifurcating branch resulting from the increase of delay. By using a second order approximation of the center manifold, we compute the first Lyapunov coefficient for Hopf bifurcation points and we show that the system under consideration can undergo a supercritical or subcritical Hopf bifurcation and the bifurcating periodic solution is stable or unstable in a neighborhood of some bifurcation points, depending on the choice of parameters.http://dx.doi.org/10.1155/2019/7609828 |
| spellingShingle | Sanaa ElFadily Abdelilah Kaddar Khalid Najib Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand International Journal of Differential Equations |
| title | Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand |
| title_full | Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand |
| title_fullStr | Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand |
| title_full_unstemmed | Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand |
| title_short | Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand |
| title_sort | direction and stability of hopf bifurcation in a delayed solow model with labor demand |
| url | http://dx.doi.org/10.1155/2019/7609828 |
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