Global stability for a forest model with unimodal fertility and monotone growth rates

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F25%3AA0000182" target="_blank" >RIV/47813059:19610/25:A0000182 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mmnp-journal.org/articles/mmnp/abs/2025/01/mmnp240144/mmnp240144.html" target="_blank" >https://www.mmnp-journal.org/articles/mmnp/abs/2025/01/mmnp240144/mmnp240144.html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/mmnp/2025016" target="_blank" >10.1051/mmnp/2025016</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Global stability for a forest model with unimodal fertility and monotone growth rates

Popis výsledku v původním jazyce

The main object of our studies is an infinite delay model b(t) = Fbt constructed and analysed in the work [Barril et al., e-print arXiv:2303.02981, https://doi.org/10.48550/arXiv.2303. 02981; Barril et al., J. Math. Biol. 88 (2024) 66] dealing with the growth of trees competing for light (with b(t) being interpreted as the population growth rate at time t). In [Barril et al. e-print arXiv:2303.02981, https://doi.org/10.48550/arXiv.2303.02981; Barril et al. [J. Math. Biol. 88 (2024) 66], the action F is defined in terms of two nonlinear monotone functions: (increasing) per capita reproduction rate β(x) of an individual of height x and (decreasing) growth rate g ϵC(R+) for the observed species of trees. As a consequence, the functional F is also monotone [Herrera and Trofimchuk, e-print arXiv:2401.08618, https://doi.org/10.48550/arXiv.2401.08618]. However, by admitting that the height of some species of trees can negatively impact the seed viability [Caraballo-Ortiz et al., J. Trop. Ecol. 27 (2011) 521-528], we should also consider hump-shaped fertility functions β. Our key finding is that in spite of this form of β, the functional F can still possess a kind of weak monotonicity property for a specific class of growth rates g. This fact assures the global attractivity of a unique positive steady state, in this way answering one of the open questions in [Herrera and Trofimchuk, 2023 MATRIX Annals, Springer (2025)].

Název v anglickém jazyce

Global stability for a forest model with unimodal fertility and monotone growth rates

Popis výsledku anglicky

The main object of our studies is an infinite delay model b(t) = Fbt constructed and analysed in the work [Barril et al., e-print arXiv:2303.02981, https://doi.org/10.48550/arXiv.2303. 02981; Barril et al., J. Math. Biol. 88 (2024) 66] dealing with the growth of trees competing for light (with b(t) being interpreted as the population growth rate at time t). In [Barril et al. e-print arXiv:2303.02981, https://doi.org/10.48550/arXiv.2303.02981; Barril et al. [J. Math. Biol. 88 (2024) 66], the action F is defined in terms of two nonlinear monotone functions: (increasing) per capita reproduction rate β(x) of an individual of height x and (decreasing) growth rate g ϵC(R+) for the observed species of trees. As a consequence, the functional F is also monotone [Herrera and Trofimchuk, e-print arXiv:2401.08618, https://doi.org/10.48550/arXiv.2401.08618]. However, by admitting that the height of some species of trees can negatively impact the seed viability [Caraballo-Ortiz et al., J. Trop. Ecol. 27 (2011) 521-528], we should also consider hump-shaped fertility functions β. Our key finding is that in spite of this form of β, the functional F can still possess a kind of weak monotonicity property for a specific class of growth rates g. This fact assures the global attractivity of a unique positive steady state, in this way answering one of the open questions in [Herrera and Trofimchuk, 2023 MATRIX Annals, Springer (2025)].

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Mathematical Modelling of Natural Phenomena

ISSN

0973-5348

e-ISSN

1760-6101

Svazek periodika

20

Číslo periodika v rámci svazku

July

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

18

Strana od-do

„18-1“-„18-18“

Kód UT WoS článku

001525278100001

EID výsledku v databázi Scopus

2-s2.0-105010910283