Geodesic
On estimates of solutions in a predator-prey model with two delays
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1697-1718

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a system of differential equations with two delays, which describes the interaction between predator and prey populations. The model takes into account the age structure of populations, herewith the delay parameters denote the time that predator and prey individuals need to become adult. We consider questions of stability of equilibrium points and study asymptotic properties of solutions. We establish estimates of solutions characterizing the stabilization rate at infinity and find estimates of attraction sets. The results are obtained using modified Lyapunov–Krasovskii functionals.
Keywords: predator-prey model, delay differential equations, asymptotic stability, estimates of solutions, attraction set, modified Lyapunov–Krasovskii functionals. 
@article{SEMR_2018_15_a110,
     author = {M. A. Skvortsova},
     title = {On estimates of solutions in a predator-prey model with two delays},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1697--1718},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a110/}
}
TY  - JOUR
AU  - M. A. Skvortsova
TI  - On estimates of solutions in a predator-prey model with two delays
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1697
EP  - 1718
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a110/
LA  - ru
ID  - SEMR_2018_15_a110
ER  - 
%0 Journal Article
%A M. A. Skvortsova
%T On estimates of solutions in a predator-prey model with two delays
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1697-1718
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a110/
%G ru
%F SEMR_2018_15_a110
M. A. Skvortsova. On estimates of solutions in a predator-prey model with two delays. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1697-1718. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a110/