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Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters. / Александров, Александр Юрьевич.

In: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, No. 3, 2024, p. 13-27.

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

Harvard

Александров, АЮ 2024, 'Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters', ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, no. 3, pp. 13-27. https://doi.org/10.21638/11701/spbu35.2024.302

APA

Александров, А. Ю. (2024). Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters. ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, (3), 13-27. https://doi.org/10.21638/11701/spbu35.2024.302

Vancouver

Александров АЮ. Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters. ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ. 2024;(3):13-27. https://doi.org/10.21638/11701/spbu35.2024.302

Author

Александров, Александр Юрьевич. / Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters. In: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ. 2024 ; No. 3. pp. 13-27.

BibTeX

@article{f43edd2e1b8d45da854460b80185bb91,
title = "Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters",
abstract = "The paper is addressed to the permanence problem for a generalized Lotka–Volterra system modeling interaction of species in a biological community. The impact of a constant delay and switching of parameters on the dynamics of the system is taken into account. Our analysis is based on the Lyapunov direct method. An original construction of a Lyapunov–Krasovskii functional is proposed. The conditions for the existence of such a functional are formulated in terms of feasibility of special systems of linear algebraic inequalities. It is proven that, under these conditions, the investigated system is permanent for any constant positive delay and any admissible switching signal. In addition, a discrete-time counterpart of the considered model is studied for which the permanence analysis is fulfilled, as well. A comparison of the obtained permanence conditions with known ones is provided. It is shown that the constraints on the system parameters derived in this paper are less conservative.",
keywords = "Lyapunov–Krasovskii functional, delay, permanence, population dynamics, switching, ultimate boundedness",
author = "Александров, {Александр Юрьевич}",
year = "2024",
doi = "10.21638/11701/spbu35.2024.302",
language = "English",
pages = "13--27",
journal = "ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ",
issn = "1817-2172",
publisher = "Электронный журнал {"}Дифференциальные уравнения и процессы управления{"}",
number = "3",

}

RIS

TY - JOUR

T1 - Permanence Analysis for Continuous and Discrete-time Generalized Lotka-Volterra Models with Delay and Switching of Parameters

AU - Александров, Александр Юрьевич

PY - 2024

Y1 - 2024

N2 - The paper is addressed to the permanence problem for a generalized Lotka–Volterra system modeling interaction of species in a biological community. The impact of a constant delay and switching of parameters on the dynamics of the system is taken into account. Our analysis is based on the Lyapunov direct method. An original construction of a Lyapunov–Krasovskii functional is proposed. The conditions for the existence of such a functional are formulated in terms of feasibility of special systems of linear algebraic inequalities. It is proven that, under these conditions, the investigated system is permanent for any constant positive delay and any admissible switching signal. In addition, a discrete-time counterpart of the considered model is studied for which the permanence analysis is fulfilled, as well. A comparison of the obtained permanence conditions with known ones is provided. It is shown that the constraints on the system parameters derived in this paper are less conservative.

AB - The paper is addressed to the permanence problem for a generalized Lotka–Volterra system modeling interaction of species in a biological community. The impact of a constant delay and switching of parameters on the dynamics of the system is taken into account. Our analysis is based on the Lyapunov direct method. An original construction of a Lyapunov–Krasovskii functional is proposed. The conditions for the existence of such a functional are formulated in terms of feasibility of special systems of linear algebraic inequalities. It is proven that, under these conditions, the investigated system is permanent for any constant positive delay and any admissible switching signal. In addition, a discrete-time counterpart of the considered model is studied for which the permanence analysis is fulfilled, as well. A comparison of the obtained permanence conditions with known ones is provided. It is shown that the constraints on the system parameters derived in this paper are less conservative.

KW - Lyapunov–Krasovskii functional

KW - delay

KW - permanence

KW - population dynamics

KW - switching

KW - ultimate boundedness

UR - https://diffjournal.spbu.ru/pdf/24302-jdecp-alexandrov.pdf

UR - https://www.mendeley.com/catalogue/322f6ddf-1b8c-3a57-8916-39134ba335e9/

U2 - 10.21638/11701/spbu35.2024.302

DO - 10.21638/11701/spbu35.2024.302

M3 - Article

SP - 13

EP - 27

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 3

ER -

ID: 125319878