Note on stability conditions for structured population dynamics models
We consider a characteristic equation to analyze asymptotic stability of a scalar renewal equation, motivated by structured population dynamics models. The characteristic equation is given by \[ 1=\int_{0}^{\infty}k(a)e^{-\lambda a}da, \] where $k:\mathbb{R}_{+}\to\mathbb{R}$ can be decomposed into...
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-09-01
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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=5298 |
| _version_ | 1797830569530228736 |
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| author | Yukihiko Nakata |
| author_facet | Yukihiko Nakata |
| author_sort | Yukihiko Nakata |
| collection | DOAJ |
| description | We consider a characteristic equation to analyze asymptotic stability of a scalar renewal equation, motivated by structured population dynamics models. The characteristic equation is given by
\[
1=\int_{0}^{\infty}k(a)e^{-\lambda a}da,
\]
where $k:\mathbb{R}_{+}\to\mathbb{R}$ can be decomposed into positive and negative parts. It is shown that if delayed negative feedback is characterized by a convex function, then all roots of the characteristic equation locate in the left half complex plane. |
| first_indexed | 2024-04-09T13:38:10Z |
| format | Article |
| id | doaj.art-44c0311b277849d9bb54d90e43856d91 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:10Z |
| publishDate | 2016-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-44c0311b277849d9bb54d90e43856d912023-05-09T07:53:06ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-09-0120167811410.14232/ejqtde.2016.1.785298Note on stability conditions for structured population dynamics modelsYukihiko Nakata0Graduate School of Mathematical Sciences, University of Tokyo, JapanWe consider a characteristic equation to analyze asymptotic stability of a scalar renewal equation, motivated by structured population dynamics models. The characteristic equation is given by \[ 1=\int_{0}^{\infty}k(a)e^{-\lambda a}da, \] where $k:\mathbb{R}_{+}\to\mathbb{R}$ can be decomposed into positive and negative parts. It is shown that if delayed negative feedback is characterized by a convex function, then all roots of the characteristic equation locate in the left half complex plane.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5298structured population dynamics modelstabilitycharacteristic equation |
| spellingShingle | Yukihiko Nakata Note on stability conditions for structured population dynamics models Electronic Journal of Qualitative Theory of Differential Equations structured population dynamics model stability characteristic equation |
| title | Note on stability conditions for structured population dynamics models |
| title_full | Note on stability conditions for structured population dynamics models |
| title_fullStr | Note on stability conditions for structured population dynamics models |
| title_full_unstemmed | Note on stability conditions for structured population dynamics models |
| title_short | Note on stability conditions for structured population dynamics models |
| title_sort | note on stability conditions for structured population dynamics models |
| topic | structured population dynamics model stability characteristic equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5298 |
| work_keys_str_mv | AT yukihikonakata noteonstabilityconditionsforstructuredpopulationdynamicsmodels |