On the stability properties of a delay differential neoclassical model of economic growth
The main aim of this paper is to establish sharp global stability conditions for the positive equilibrium of a well-known model of economic growth when a delay is considered in the production function. In order to deal with a broad scenario, we establish some results of global attraction for a gener...
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| Format: | Article |
| Language: | English |
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University of Szeged
2018-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6361 |
| _version_ | 1797830523784003584 |
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| author | Sebastián Buedo-Fernández Eduardo Liz |
| author_facet | Sebastián Buedo-Fernández Eduardo Liz |
| author_sort | Sebastián Buedo-Fernández |
| collection | DOAJ |
| description | The main aim of this paper is to establish sharp global stability conditions for the positive equilibrium of a well-known model of economic growth when a delay is considered in the production function. In order to deal with a broad scenario, we establish some results of global attraction for a general family of differential equations with variable delay; for it, we use the notion of strong attractor, which allows us to simplify the proofs, as well as to generalize previous results. Our study reveals that sometimes production delays are not able to destabilize the positive equilibrium, even if they are large. In other cases, the stability properties of the equilibrium depend on the interaction between the delay and other relevant model parameters, leading sometimes to stability windows in the bifurcation diagram. |
| first_indexed | 2024-04-09T13:38:32Z |
| format | Article |
| id | doaj.art-92c08befd98d4d31b68be746833685d7 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:32Z |
| publishDate | 2018-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-92c08befd98d4d31b68be746833685d72023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-06-0120184311410.14232/ejqtde.2018.1.436361On the stability properties of a delay differential neoclassical model of economic growthSebastián Buedo-Fernández0Eduardo Liz1Universidade de Santiago de Compostela, Santiago de Compostela, SpainUniversity of Vigo, Vigo, SpainThe main aim of this paper is to establish sharp global stability conditions for the positive equilibrium of a well-known model of economic growth when a delay is considered in the production function. In order to deal with a broad scenario, we establish some results of global attraction for a general family of differential equations with variable delay; for it, we use the notion of strong attractor, which allows us to simplify the proofs, as well as to generalize previous results. Our study reveals that sometimes production delays are not able to destabilize the positive equilibrium, even if they are large. In other cases, the stability properties of the equilibrium depend on the interaction between the delay and other relevant model parameters, leading sometimes to stability windows in the bifurcation diagram.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6361delay differential equationneoclassical growth modelglobal stabilitystability switcheslasota equationgamma-ricker map |
| spellingShingle | Sebastián Buedo-Fernández Eduardo Liz On the stability properties of a delay differential neoclassical model of economic growth Electronic Journal of Qualitative Theory of Differential Equations delay differential equation neoclassical growth model global stability stability switches lasota equation gamma-ricker map |
| title | On the stability properties of a delay differential neoclassical model of economic growth |
| title_full | On the stability properties of a delay differential neoclassical model of economic growth |
| title_fullStr | On the stability properties of a delay differential neoclassical model of economic growth |
| title_full_unstemmed | On the stability properties of a delay differential neoclassical model of economic growth |
| title_short | On the stability properties of a delay differential neoclassical model of economic growth |
| title_sort | on the stability properties of a delay differential neoclassical model of economic growth |
| topic | delay differential equation neoclassical growth model global stability stability switches lasota equation gamma-ricker map |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6361 |
| work_keys_str_mv | AT sebastianbuedofernandez onthestabilitypropertiesofadelaydifferentialneoclassicalmodelofeconomicgrowth AT eduardoliz onthestabilitypropertiesofadelaydifferentialneoclassicalmodelofeconomicgrowth |