Asymptotic Behavior of Solutions to a Delay Integro-Differential Equation Arising in Models of Living Systems

Asymptotic Behavior of Solutions to a Delay Integro-Differential Equation Arising in Models of Living Systems Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2021, Volume: 31, Number: 2, Pages: 131-146 Pages count : 16 DOI: 10.1134/S1055134421020036

Tags

asymptotic behavior of solutions; boundedness of solutions; delay integro-differential equation; mathematical model of a living system; stability of equilibria

Authors

Loginov K.K. ¹ , Pertsev N.V. ¹

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation

Abstract: We consider a mathematical model describing the production of the components of someliving system under the influence of positive and negative feedback. The model is presented in theform of the Cauchy problem for a nonlinear delay integro-differential equation. A theoremof the existence, uniqueness, and nonnegativity of the solutions to the model on the half-axis isproved for nonnegative initial data. The questions of the asymptotic behavior of the solutions andthe stability of the equilibria of the model are investigated. Sufficient conditions for the asymptoticstability are obtained for nontrivial equilibria and the boundaries of their attraction domains areestimated. Examples illustrating the application of the obtained theoretical results are given. © 2021, Pleiades Publishing, Ltd.

Loginov K.K. , Pertsev N.V.
Asymptotic Behavior of Solutions to a Delay Integro-Differential Equation Arising in Models of Living Systems
Siberian Advances in Mathematics. 2021. V.31. N2. P.131-146. DOI: 10.1134/S1055134421020036 Scopus OpenAlex

Scopus:	2-s2.0-85107323965
OpenAlex:	W3179654890

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Scopus	1