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Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay. / Ekimov, A. V.; Chizhova, O. N.; Zaranik, U. P.

In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Vol. 15, No. 4, 01.01.2019, p. 415-424.

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

Harvard

Ekimov, AV, Chizhova, ON & Zaranik, UP 2019, 'Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay.', Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, vol. 15, no. 4, pp. 415-424. https://doi.org/10.21638/11702/spbu10.2019.401

APA

Ekimov, A. V., Chizhova, O. N., & Zaranik, U. P. (2019). Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, 15(4), 415-424. https://doi.org/10.21638/11702/spbu10.2019.401

Vancouver

Ekimov AV, Chizhova ON, Zaranik UP. Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2019 Jan 1;15(4):415-424. https://doi.org/10.21638/11702/spbu10.2019.401

Author

Ekimov, A. V. ; Chizhova, O. N. ; Zaranik, U. P. / Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay. In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2019 ; Vol. 15, No. 4. pp. 415-424.

BibTeX

@article{945175bac0714957aefea3193d759c15,
title = "Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay.",
abstract = "These systems can be considered as a model for the spread of the epidemic in the population. In addition, systems with linearly increasing delay describe the dynamics of the information server, mixing tank, the process of formation of traffic jams on the ring road, etc. For the study, the concept of an average system is introduced. This approach allows us to reduce the analysis of the Lyapunov stability problem of the zero solution of the original system to the investigation of the zero solution of the averaged system. Sufficient conditions for stationary system stability are formulated. Then the application of Razumihin's approach to the study of stability original system is used. The Lyapunov function is constructed. As a result, new sufficient conditions for the asymptotic stability of the zero solution of nonstationary homogeneous systems with a linearly increasing time delay are obtained. These conditions are the generalization of well-known results for the linear systems with a linearly increasing time delay.",
keywords = "Asymptotic stability, Homogeneous differential-difference system, Linearly increasing time delay",
author = "Ekimov, {A. V.} and Chizhova, {O. N.} and Zaranik, {U. P.}",
year = "2019",
month = jan,
day = "1",
doi = "10.21638/11702/spbu10.2019.401",
language = "English",
volume = "15",
pages = "415--424",
journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",
issn = "1811-9905",
publisher = "Издательство Санкт-Петербургского университета",
number = "4",

}

RIS

TY - JOUR

T1 - Stability of homogeneous nonstationary systems of differential-difference equations with linearly time delay.

AU - Ekimov, A. V.

AU - Chizhova, O. N.

AU - Zaranik, U. P.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - These systems can be considered as a model for the spread of the epidemic in the population. In addition, systems with linearly increasing delay describe the dynamics of the information server, mixing tank, the process of formation of traffic jams on the ring road, etc. For the study, the concept of an average system is introduced. This approach allows us to reduce the analysis of the Lyapunov stability problem of the zero solution of the original system to the investigation of the zero solution of the averaged system. Sufficient conditions for stationary system stability are formulated. Then the application of Razumihin's approach to the study of stability original system is used. The Lyapunov function is constructed. As a result, new sufficient conditions for the asymptotic stability of the zero solution of nonstationary homogeneous systems with a linearly increasing time delay are obtained. These conditions are the generalization of well-known results for the linear systems with a linearly increasing time delay.

AB - These systems can be considered as a model for the spread of the epidemic in the population. In addition, systems with linearly increasing delay describe the dynamics of the information server, mixing tank, the process of formation of traffic jams on the ring road, etc. For the study, the concept of an average system is introduced. This approach allows us to reduce the analysis of the Lyapunov stability problem of the zero solution of the original system to the investigation of the zero solution of the averaged system. Sufficient conditions for stationary system stability are formulated. Then the application of Razumihin's approach to the study of stability original system is used. The Lyapunov function is constructed. As a result, new sufficient conditions for the asymptotic stability of the zero solution of nonstationary homogeneous systems with a linearly increasing time delay are obtained. These conditions are the generalization of well-known results for the linear systems with a linearly increasing time delay.

KW - Asymptotic stability

KW - Homogeneous differential-difference system

KW - Linearly increasing time delay

UR - http://www.scopus.com/inward/record.url?scp=85082072660&partnerID=8YFLogxK

U2 - 10.21638/11702/spbu10.2019.401

DO - 10.21638/11702/spbu10.2019.401

M3 - Article

AN - SCOPUS:85082072660

VL - 15

SP - 415

EP - 424

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 4

ER -

ID: 60765200