Abstract:
In the paper we consider a system of nonlinear differential equations with distributed delay and periodic coefficients in linear terms. Sufficient conditions for exponential stability of the zero solution are established, estimates that characterize the rate of decay of solutions at infinity are obtained, and attraction sets of the zero solution are indicated. Similar results are obtained in the case of small perturbations in linear terms.
Keywords:
exponential stability, Lyapunov - Krasovskii functional, nonlinear equation, distributed delay, periodic coefficients, perturbations in linear terms.
Citation:
T. Yskak, “Estimates for solutions of one class to systems of nonlinear differential equations with distributed delay”, Sib. Èlektron. Mat. Izv., 17 (2020), 2204–2215
\Bibitem{Ysk20}
\by T.~Yskak
\paper Estimates for solutions of one class to systems of nonlinear differential equations with distributed delay
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 2204--2215
\mathnet{http://mi.mathnet.ru/semr1340}
\crossref{https://doi.org/10.33048/semi.2020.17.146}
Linking options:
https://www.mathnet.ru/eng/semr1340
https://www.mathnet.ru/eng/semr/v17/p2204
This publication is cited in the following 5 articles:
T. K. Iskakov, M. A. Skvortsova, “Estimates for Solutions of a Biological Model with Infinite Distributed Delay”, Comput. Math. and Math. Phys., 64:8 (2024), 1689
I. I. Matveeva, “Ustoichivost reshenii odnogo klassa nelineinykh sistem integro-differentsialnykh uravnenii s zapazdyvaniem”, Chelyab. fiz.-matem. zhurn., 9:4 (2024), 609–621
T. K. Yskak, “Ustoichivost reshenii sistem nelineinykh differentsialnykh uravnenii s beskonechnym raspredelennym zapazdyvaniem”, Chelyab. fiz.-matem. zhurn., 8:4 (2023), 542–552
M. A. Skvortsova, T. Yskak, “Otsenki reshenii differentsialnykh uravnenii s raspredelennym zapazdyvaniem, opisyvayuschikh konkurentsiyu neskolkikh vidov mikroorganizmov”, Sib. zhurn. industr. matem., 25:4 (2022), 193–205
M. A. Skvortsova, T. Yskak, “Estimates of Solutions to Differential Equations with Distributed Delay Describing the Competition of Several Types of Microorganisms”, J. Appl. Ind. Math., 16:4 (2022), 800
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