Geodesic
Stability of solutions in the predator-prey model with delay
Matematičeskie zametki SVFU, Tome 23 (2016) no. 2, pp. 108-120 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a system of delay differential equations describing the interaction between two populations the predators and prey. We study the asymptotic stability of stationary solutions to this system. Using the modified Lyapunov-Krasovskii functional we establish estimates for solutions characterizing the rate of convergence to the stationary solutions.
Keywords: predator-prey model, delay differential equations, asymptotic stability, characteristic quasipolynomial, estimates for solutions, modified Lyapunov-Krasovskii functional. 
@article{SVFU_2016_23_2_a7,
     author = {M. A. Skvortsova},
     title = {Stability of solutions in the predator-prey model with delay},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {108--120},
     year = {2016},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a7/}
}
TY  - JOUR
AU  - M. A. Skvortsova
TI  - Stability of solutions in the predator-prey model with delay
JO  - Matematičeskie zametki SVFU
PY  - 2016
SP  - 108
EP  - 120
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a7/
LA  - ru
ID  - SVFU_2016_23_2_a7
ER  - 
%0 Journal Article
%A M. A. Skvortsova
%T Stability of solutions in the predator-prey model with delay
%J Matematičeskie zametki SVFU
%D 2016
%P 108-120
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a7/
%G ru
%F SVFU_2016_23_2_a7
M. A. Skvortsova. Stability of solutions in the predator-prey model with delay. Matematičeskie zametki SVFU, Tome 23 (2016) no. 2, pp. 108-120. http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a7/

[1] Forde J. E., Delay differential equation models in mathematical biology, Thes.. doct. philosophy., Univ. Michigan, 2005 | MR

[2] Krasovskii N. N., Stability of motion, Stanford Uni. Press, Stanford, CA, 1959 | MR

[3] Elsgoltz L. E. and Norkin S. B., Introduction to the theory of differential equations with deviating argument, Nauka, Moscow, 1971 | MR

[4] Chebotarev N. G. and Meiman N. N., “Raus–Gurvitz problem for polynomials and entire functions”, Tr. Steklov Math. Inst., 26 (1949), 3–331 | MR

[5] Khusainov D. Ya., Ivanov A. F., and Kozhametov A. T., “Convergence estimates for solutions of linear stationary systems of differential-difference equations with constant delay”, Differ. Equ., 41:8 (2005), 1196–1200 | DOI | MR | MR | Zbl

[6] Kharitonov V. L., Hinrichsen D., “Exponential estimates for time delay systems”, Syst. Control Lett, 53:5 (2004), 395–405 | DOI | MR | Zbl

[7] Mondié S., Kharitonov V. L., “Exponential estimates for retarded time-delay systems: LMI approach”, IEEE Trans. Autom. Control, 50:2 (2005), 268–273 | DOI | MR | Zbl

[8] Demidenko G. V. and Matveeva I. I., “Asymptotic properties of solutions to differential equations with delay argument”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 5:3 (2005), 20–28 | Zbl

[9] Demidenko G. V., Matrix equations, Izdat. Novosib. Gos. Univ., Novosibirsk, 2009