We consider a mathematical model describing the production of the components of some living system under the influence of positive and negative feedback. The model is presented in the form of the Cauchy problem for a nonlinear delay integro-differential equation. A theorem of the existence, uniqueness, and nonnegativity of the solutions to the model on the half-axis is proved for nonnegative initial data. The questions of the asymptotic behavior of the solutions and the stability of the equilibria of the model are investigated. Sufficient conditions for the asymptotic stability are obtained for nontrivial equilibria and the boundaries of their attraction domains are estimated. Examples illustrating the application of the obtained theoretical results are given.
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The authors were financially supported by the Russian Foundation for Basic Research (project no. 18–29–10086).
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Loginov, K.K., Pertsev, N.V. Asymptotic Behavior of Solutions to a Delay Integro-Differential Equation Arising in Models of Living Systems. Sib. Adv. Math. 31, 131–146 (2021). https://doi.org/10.1134/S1055134421020036
- delay integro-differential equation
- boundedness of solutions
- asymptotic behavior of solutions
- stability of equilibria
- mathematical model of a living system