Geodesic
Estimates of solutions in the model of interaction of populations with several delays
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 84-105

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We consider a system of differential equations with several delays, which describes the interaction of $n$ species of microorganisms. We obtain sufficient conditions for the asymptotic stability of a nontrivial equilibrium state corresponding to the partial survival of populations. We establish estimates of solutions that characterize the rate of stabilization at infinity and indicate estimates of the attraction set of a given equilibrium state. The results are obtained by using the modified Lyapunov–Krasovsky functional.
Keywords: model of interaction of populations, equation with retarded argument, asymptotic stability, estimate of solution, attraction set, modified Lyapunov–Krasovsky functional. 
@article{INTO_2020_188_a7,
     author = {M. A. Skvortsova},
     title = {Estimates of solutions in the model of interaction of populations with several delays},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {84--105},
     publisher = {mathdoc},
     volume = {188},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_188_a7/}
}
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M. A. Skvortsova. Estimates of solutions in the model of interaction of populations with several delays. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 84-105. http://geodesic.mathdoc.fr/item/INTO_2020_188_a7/