Global stability for a forest model with unimodal fertility and monotone growth rates
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Global stability for a forest model with unimodal fertility and monotone growth rates
Original language description
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)].
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Modelling of Natural Phenomena
ISSN
0973-5348
e-ISSN
1760-6101
Volume of the periodical
20
Issue of the periodical within the volume
July
Country of publishing house
FR - FRANCE
Number of pages
18
Pages from-to
„18-1“-„18-18“
UT code for WoS article
001525278100001
EID of the result in the Scopus database
2-s2.0-105010910283