Asymptotic stability of delayed consumer age-structured population models with an Allee effect

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12310%2F18%3A43897649" target="_blank" >RIV/60076658:12310/18:43897649 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/60077344:_____/18:00496118

Výsledek na webu

<a href="https://reader.elsevier.com/reader/sd/pii/S0025556418301044?token=8615B6822ED2F35AC3A7E01518BA4BAF361C39CEFFFFE175800658837CDF90E233DED995336672A09071FD42D26972BB" target="_blank" >https://reader.elsevier.com/reader/sd/pii/S0025556418301044?token=8615B6822ED2F35AC3A7E01518BA4BAF361C39CEFFFFE175800658837CDF90E233DED995336672A09071FD42D26972BB</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.mbs.2018.10.001" target="_blank" >10.1016/j.mbs.2018.10.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotic stability of delayed consumer age-structured population models with an Allee effect

Popis výsledku v původním jazyce

In this article we study a nonlinear age-structured consumer population model with density-dependent death and fertility rates, and time delays that model incubation/gestation period. Density dependence we consider combines both positive effects at low population numbers (i.e., the Allee effect) and negative effects at high population numbers due to infra-specific competition of consumers. The positive density-dependence is either due to an increase in the birth rate, or due to a decrease in the mortality rate at low population numbers. We prove that similarly to unstructured models, the Allee effect leads to model multi-stability where, besides the locally stable extinction equilibrium, there are up to two positive equilibria. Calculating derivatives of the basic reproduction number at the equilibria we prove that the upper of the two non-trivial equilibria (when it exists) is locally asymptotically stable independently of the time delay. The smaller of the two equilibria is always unstable. Using numerical simulations we analyze topologically nonequivalent phase portraits of the model.

Název v anglickém jazyce

Asymptotic stability of delayed consumer age-structured population models with an Allee effect

Popis výsledku anglicky

In this article we study a nonlinear age-structured consumer population model with density-dependent death and fertility rates, and time delays that model incubation/gestation period. Density dependence we consider combines both positive effects at low population numbers (i.e., the Allee effect) and negative effects at high population numbers due to infra-specific competition of consumers. The positive density-dependence is either due to an increase in the birth rate, or due to a decrease in the mortality rate at low population numbers. We prove that similarly to unstructured models, the Allee effect leads to model multi-stability where, besides the locally stable extinction equilibrium, there are up to two positive equilibria. Calculating derivatives of the basic reproduction number at the equilibria we prove that the upper of the two non-trivial equilibria (when it exists) is locally asymptotically stable independently of the time delay. The smaller of the two equilibria is always unstable. Using numerical simulations we analyze topologically nonequivalent phase portraits of the model.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10602 - Biology (theoretical, mathematical, thermal, cryobiology, biological rhythm), Evolutionary biology

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Biosciences

ISSN

0025-5564

e-ISSN

—

Svazek periodika

306

Číslo periodika v rámci svazku

DEC 2018

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

170-179

Kód UT WoS článku

000453496200017

EID výsledku v databázi Scopus

2-s2.0-85054598285