Discrete or distributed delay? Effects on stability of population growth
The growth of a population subject to maturation delay is modeled by using either a discrete delay or a delay continuously distributed over the population. The occurrence of stability switches (stable-unstable-stable) of the positive equilibrium as the delay increases is investigated in both cases....
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.19 |
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| _version_ | 1832590125402423296 |
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| author | Edoardo Beretta Dimitri Breda |
| author_facet | Edoardo Beretta Dimitri Breda |
| author_sort | Edoardo Beretta |
| collection | DOAJ |
| description | The growth of a population subject to maturation delay is modeled by using either a discrete delay or a delay continuously distributed over the population. The occurrence of stability switches (stable-unstable-stable) of the positive equilibrium as the delay increases is investigated in both cases. Necessary and sufficient conditions are provided by analyzing the relevant characteristic equations. It is shown that for any choice of parameter values for which the discrete delay model presents stability switches there exists a maximum delay variance beyond which no switch occurs for the continuous delay model: the delay variance has a stabilizing effect. Moreover, it is illustrated how, in the presence of switches, the unstable delay domain is as larger as lower is the ratio between the juveniles and the adults mortality rates. |
| format | Article |
| id | doaj-art-7939df492ed64a86b6cc6b752a302c0f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7939df492ed64a86b6cc6b752a302c0f2025-01-24T02:34:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-01131194110.3934/mbe.2016.13.19Discrete or distributed delay? Effects on stability of population growthEdoardo Beretta0Dimitri Breda1CIMAB, University of Milano, via C. Saldini 50, I20133 MilanoDepartment of Mathematics and Computer Science, University of Udine, via delle Scienze 206, I33100 UdineThe growth of a population subject to maturation delay is modeled by using either a discrete delay or a delay continuously distributed over the population. The occurrence of stability switches (stable-unstable-stable) of the positive equilibrium as the delay increases is investigated in both cases. Necessary and sufficient conditions are provided by analyzing the relevant characteristic equations. It is shown that for any choice of parameter values for which the discrete delay model presents stability switches there exists a maximum delay variance beyond which no switch occurs for the continuous delay model: the delay variance has a stabilizing effect. Moreover, it is illustrated how, in the presence of switches, the unstable delay domain is as larger as lower is the ratio between the juveniles and the adults mortality rates.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.19stability switches.$\delta$-dirac distributiongamma distributionpopulation growthlocal asymptotic stability analysismaturation delay |
| spellingShingle | Edoardo Beretta Dimitri Breda Discrete or distributed delay? Effects on stability of population growth Mathematical Biosciences and Engineering stability switches. $\delta$-dirac distribution gamma distribution population growth local asymptotic stability analysis maturation delay |
| title | Discrete or distributed delay? Effects on stability of population growth |
| title_full | Discrete or distributed delay? Effects on stability of population growth |
| title_fullStr | Discrete or distributed delay? Effects on stability of population growth |
| title_full_unstemmed | Discrete or distributed delay? Effects on stability of population growth |
| title_short | Discrete or distributed delay? Effects on stability of population growth |
| title_sort | discrete or distributed delay effects on stability of population growth |
| topic | stability switches. $\delta$-dirac distribution gamma distribution population growth local asymptotic stability analysis maturation delay |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.19 |
| work_keys_str_mv | AT edoardoberetta discreteordistributeddelayeffectsonstabilityofpopulationgrowth AT dimitribreda discreteordistributeddelayeffectsonstabilityofpopulationgrowth |