Geodesic
Construction of exponentially decreasing estimates of solutions to a Cauchy problem for some nonlinear systems of delay differential equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 579-598

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The behavior of solutions for several models of living systems, presented as the Cauchy problem for nonlinear systems of delay differential equations, is investigated. A set of conditions providing exponentially decreasing estimates of the components of the solutions of the studied Cauchy problem is established. The parameters of exponential estimates are found as a solution of a nonlinear system of inequalities, based on the right part of the system of differential equations. Results of the studies on mathematical models arising in epidemiology, immunology, and physiology are presented.
Keywords: delay differential equations, initial problem, non-negative solutions, exponentially decreasing estimates of the solutions, mathematical models of living systems.
Mots-clés : M-matrix 
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     author = {N. V. Pertsev},
     title = {Construction of exponentially decreasing estimates of solutions to a {Cauchy} problem for some nonlinear systems of delay differential equations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {579--598},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a31/}
}
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N. V. Pertsev. Construction of exponentially decreasing estimates of solutions to a Cauchy problem for some nonlinear systems of delay differential equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 579-598. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a31/