The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model
A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/901014 |
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| _version_ | 1832550188964642816 |
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| author | Carlo Bianca Massimiliano Ferrara Luca Guerrini |
| author_facet | Carlo Bianca Massimiliano Ferrara Luca Guerrini |
| author_sort | Carlo Bianca |
| collection | DOAJ |
| description | A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results. |
| format | Article |
| id | doaj-art-0a8b19625a4747ce85e8c2f410049a90 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0a8b19625a4747ce85e8c2f410049a902025-02-03T06:07:19ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/901014901014The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth ModelCarlo Bianca0Massimiliano Ferrara1Luca Guerrini2Dipartimento di Scienze Matematiche, Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, ItalyDepartment of Law and Economics, University Mediterranea of Reggio Calabria and CRIOS University Bocconi of Milan, Via dei Bianchi 2, 89127 Reggio Calabria, ItalyDepartment of Management, Polytechnic University of Marche, 60121 Ancona, ItalyA further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results.http://dx.doi.org/10.1155/2013/901014 |
| spellingShingle | Carlo Bianca Massimiliano Ferrara Luca Guerrini The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model Abstract and Applied Analysis |
| title | The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model |
| title_full | The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model |
| title_fullStr | The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model |
| title_full_unstemmed | The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model |
| title_short | The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model |
| title_sort | time delays effects on the qualitative behavior of an economic growth model |
| url | http://dx.doi.org/10.1155/2013/901014 |
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