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EnglishThe 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.
Discrete or distributed delay? Effects on stability of population growth / Beretta, Edoardo; Breda, Dimitri. - In: MATHEMATICAL BIOSCIENCES AND ENGINEERING. - ISSN 1547-1063. - STAMPA. - 13:1(2016), pp. 19-41.
| Titolo: | Discrete or distributed delay? Effects on stability of population growth |
| Autori: | |
| Data di pubblicazione: | 2016 |
| Rivista: | |
| Citazione: | Discrete or distributed delay? Effects on stability of population growth / Beretta, Edoardo; Breda, Dimitri. - In: MATHEMATICAL BIOSCIENCES AND ENGINEERING. - ISSN 1547-1063. - STAMPA. - 13:1(2016), pp. 19-41. |
| Abstract: | 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. |
| Handle: | http://hdl.handle.net/11390/1070154 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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| GAMMA_delay.pdf | articolo principale, post referaggio | Documento in Post-print | Non pubblico | Accesso ristretto Richiedi una copia |
http://hdl.handle.net/11390/1070154
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