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On estimates of solutions in a predator-prey model with two delays. / Skvortsova, Maria Aleksandrovna.

In: Сибирские электронные математические известия, Vol. 15, 01.01.2018, p. 1697-1718.

Research output: Contribution to journal › Article › peer-review

Harvard

Skvortsova, MA 2018, 'On estimates of solutions in a predator-prey model with two delays', Сибирские электронные математические известия, vol. 15, pp. 1697-1718. https://doi.org/10.33048/semi.2018.15.141

APA

Skvortsova, M. A. (2018). On estimates of solutions in a predator-prey model with two delays. Сибирские электронные математические известия, 15, 1697-1718. https://doi.org/10.33048/semi.2018.15.141

Vancouver

Skvortsova MA. On estimates of solutions in a predator-prey model with two delays. Сибирские электронные математические известия. 2018 Jan 1;15:1697-1718. doi: 10.33048/semi.2018.15.141

Author

Skvortsova, Maria Aleksandrovna. / On estimates of solutions in a predator-prey model with two delays. In: Сибирские электронные математические известия. 2018 ; Vol. 15. pp. 1697-1718.

BibTeX

@article{93e1ad5a77444ff9acb35b98c31e457f,
title = "On estimates of solutions in a predator-prey model with two delays",
abstract = "We consider a system of differential equations with two delays, which describes the interaction between predator and prey populations. The model takes into account the age structure of populations, herewith the delay parameters denote the time that predator and prey individuals need to become adult. We consider questions of stability of equilibrium points and study asymptotic properties of solutions. We establish estimates of solutions characterizing the stabilization rate at infinity and find estimates of attraction sets. The results are obtained using modified Lyapunov-Krasovskii functionals.",
keywords = "Asymptotic stability, Attraction set, Delay differential equations, Estimates of solutions, Modified Lyapunov- Krasovskii functionals, Predator-prey model",
author = "Skvortsova, {Maria Aleksandrovna}",
year = "2018",
month = jan,
day = "1",
doi = "10.33048/semi.2018.15.141",
language = "English",
volume = "15",
pages = "1697--1718",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - On estimates of solutions in a predator-prey model with two delays

AU - Skvortsova, Maria Aleksandrovna

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We consider a system of differential equations with two delays, which describes the interaction between predator and prey populations. The model takes into account the age structure of populations, herewith the delay parameters denote the time that predator and prey individuals need to become adult. We consider questions of stability of equilibrium points and study asymptotic properties of solutions. We establish estimates of solutions characterizing the stabilization rate at infinity and find estimates of attraction sets. The results are obtained using modified Lyapunov-Krasovskii functionals.

AB - We consider a system of differential equations with two delays, which describes the interaction between predator and prey populations. The model takes into account the age structure of populations, herewith the delay parameters denote the time that predator and prey individuals need to become adult. We consider questions of stability of equilibrium points and study asymptotic properties of solutions. We establish estimates of solutions characterizing the stabilization rate at infinity and find estimates of attraction sets. The results are obtained using modified Lyapunov-Krasovskii functionals.

KW - Asymptotic stability

KW - Attraction set

KW - Delay differential equations

KW - Estimates of solutions

KW - Modified Lyapunov- Krasovskii functionals

KW - Predator-prey model

UR - http://www.scopus.com/inward/record.url?scp=85074903006&partnerID=8YFLogxK

U2 - 10.33048/semi.2018.15.141

DO - 10.33048/semi.2018.15.141

M3 - Article

AN - SCOPUS:85074903006

VL - 15

SP - 1697

EP - 1718

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 22320268