On the local stability of a population dynamics model with delay
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 951-957.

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

We study the local stability of an integro-differential equation with aftereffect, which is a model of the dynamics of a stage-dependent one-species population.
Keywords: linear functional-differential equation, aftereffect, asymptotic stability, stability in parameter space, population dynamics, stage-dependent model.
@article{SEMR_2014_11_a74,
     author = {V. V. Malygina and M. V. Mulyukov and N. V. Pertsev},
     title = {On the local stability of a population dynamics model with delay},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {951--957},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a74/}
}
TY  - JOUR
AU  - V. V. Malygina
AU  - M. V. Mulyukov
AU  - N. V. Pertsev
TI  - On the local stability of a population dynamics model with delay
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2014
SP  - 951
EP  - 957
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2014_11_a74/
LA  - ru
ID  - SEMR_2014_11_a74
ER  - 
%0 Journal Article
%A V. V. Malygina
%A M. V. Mulyukov
%A N. V. Pertsev
%T On the local stability of a population dynamics model with delay
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2014
%P 951-957
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2014_11_a74/
%G ru
%F SEMR_2014_11_a74
V. V. Malygina; M. V. Mulyukov; N. V. Pertsev. On the local stability of a population dynamics model with delay. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 951-957. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a74/

[1] S. Busenberg, K. Cooke, “The Effect of Integral Conditions in Certain Equations Modelling Epidemics and Population Growth”, J. Math. Biol., 10 (1980), 13–32 | DOI | MR | Zbl

[2] H. W. Hethcote, H. W. Stech, P. van den Driessche, “Stability analisys for models of diseases without immunity”, J. Math. Biol., 13 (1981), 185–198 | DOI | MR | Zbl

[3] J. Belair, “Lifespans in Population Models: Using Time Delay”, Lecture Notes in Biomathematics, Springer, New York, 1991, 16–27 | DOI | MR

[4] W. G. Aiello, H. I. Freedman, J. Wu, “Analysis of a model representing stage-structured population growth with state-dependent time delay”, SIAM J. Appl. Math., 52:3 (1992), 855–869 | DOI | MR | Zbl

[5] N. V. Pertsev, “Bounded solutions for a class of systems of integral equations arising in models of biological processes”, Diff. Equ., 35:6 (1999), 835–840 | MR | Zbl

[6] N. V. Pertsev, “On the stability of the zero solution of a system of integrodifferential equations that arise in models of population dynamics”, Russian Math. (Iz. VUZ), 43:8 (1999), 44–49 | MR | Zbl

[7] G. Bocharov, K. Hadeler, “Structured Population Models, Conservation Laws and Delay Equations”, J. Diff. Equ., 168 (2000), 212–237 | DOI | MR | Zbl

[8] G. Bocharov, F. Rihan, “Numerical modelling in biosciences using delay differential equations”, J. Comput. Appl. Math., 125 (2000), 183–199 | DOI | MR | Zbl

[9] I. A. Tarasov, N. V. Pertsev, “Analiz reshenii integrodifferentsialnogo uravneniya, voznikayuschego v dinamike populyatsii”, Vestnik Omsk. un-ta, 2003, no. 2, 13–15 | MR | Zbl

[10] A. A. Andronov, A. T. Maier, “Prosteishie lineinye sistemy s zapazdyvaniem”, Avtomatika i telemekhanika, 1946, no. 7, 95–106 | MR | Zbl

[11] A. D. Myshkis, Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972 | MR | Zbl

[12] L. E. Elsgolts, S. B. Norkin, Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1971 | MR

[13] N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991 | MR | Zbl

[14] V. B. Kolmanovskii, V. R. Nosov, Ustoichivost i periodicheskie rezhimy reguliruemykh sistem s posledeistviem, Nauka, M., 1981 | MR

[15] B. S. Razumikhin, Ustoichivost ereditarnykh sistem, Nauka, M., 1986 | MR

[16] A. Yu. Obolenskii, “Ob ustoichivosti reshenii avtonomnykh sistem Vazhevskogo s zapazdyvaniem”, Ukrainskii matematicheskii zhurnal, 35 (1983), 574–579 | MR | Zbl

[17] R. Volz, “Stability Conditions for Systems of Linear Nonautonomous Delay Differential Equations”, J. Math. Anal. Appl., 120:2 (1986), 584–595 | DOI | MR | Zbl

[18] V. V. Malygina, T. L. Sabatulina, “Ustoichivost funktsionalno-differentsialnykh uravnenii s ogranichennym posledeistviem”, Izv. vuzov. Matematika, 2014, no. 4, 25–41 | Zbl

[19] R. Bellman, K. L. Kuk, Differentsialno-raznostnye uravneniya, Mir, M., 1967 | MR | Zbl

[20] T. Luzyanina, D. Roose, G. Bocharov, “Numerical bifurcation analysis of immunological models with time delays”, J. Comput. Appl. Math., 184 (2005), 165–176 | DOI | MR | Zbl

[21] Yu. I. Neimark, Dinamicheskie sistemy i upravlyaemye protsessy, Nauka, M., 1978 | MR