Behavior of solutions of a~dissipative integral Lotka-Volterra model
Sibirskij žurnal industrialʹnoj matematiki, Tome 6 (2003) no. 2, pp. 95-106.

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

@article{SJIM_2003_6_2_a8,
     author = {N. V. Pertsev and A. N. Pichugina and B. Yu. Pichugin},
     title = {Behavior of solutions of a~dissipative integral {Lotka-Volterra} model},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {95--106},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2003_6_2_a8/}
}
TY  - JOUR
AU  - N. V. Pertsev
AU  - A. N. Pichugina
AU  - B. Yu. Pichugin
TI  - Behavior of solutions of a~dissipative integral Lotka-Volterra model
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2003
SP  - 95
EP  - 106
VL  - 6
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2003_6_2_a8/
LA  - ru
ID  - SJIM_2003_6_2_a8
ER  - 
%0 Journal Article
%A N. V. Pertsev
%A A. N. Pichugina
%A B. Yu. Pichugin
%T Behavior of solutions of a~dissipative integral Lotka-Volterra model
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2003
%P 95-106
%V 6
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2003_6_2_a8/
%G ru
%F SJIM_2003_6_2_a8
N. V. Pertsev; A. N. Pichugina; B. Yu. Pichugin. Behavior of solutions of a~dissipative integral Lotka-Volterra model. Sibirskij žurnal industrialʹnoj matematiki, Tome 6 (2003) no. 2, pp. 95-106. http://geodesic.mathdoc.fr/item/SJIM_2003_6_2_a8/

[1] Sharpe F. R., Lotka A. J., “A problem of age-distribution”, Philos. Mag., 21 (1911), 435–438

[2] MacKendrick A. G., “Applications of mathematics to medical problems”, Proc. Edinburg Math. Soc., 40 (1926), 98–130

[3] Lotka A. J., “A contribution to the theory of self-renewing aggregates, with special reference to industrial replacement”, Ann. Math. Statist., 10 (1939), 1–25 | DOI | Zbl

[4] Gurtin M. E., MacCamy R. C., “Non-linearage-dep endent population dynamics”, Arch. Rational Mech. Anal., 54 (1974), 281–300 | DOI | MR | Zbl

[5] Swick S. E., “On nonlinearage-dep endentmodel of single species population dynamics”, SIAM J. Appl. Math., 32:2 (1977), 484–498 | DOI | MR | Zbl

[6] Cushing J. M., Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics, Springer, New York, 1977 | MR

[7] Webb G. F., Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, New York; Basel, 1985 | MR | Zbl

[8] Aiello W. G., Freedman H. I., Wu J., “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

[9] Bocharov G., Hadeler K. P., “Structured populationmodels, conservation laws and delay equations”, J. Differential Equations, 168 (2000), 212–237 | DOI | MR | Zbl

[10] Kolmogorov A. N., “Kachestvennoe izuchenie matematicheskikh modelei dinamiki populyatsii”, Problemy kibernetiki, 1972, no. 25, 100–106 | MR

[11] Volterra V., Matematicheskaya teoriya borby za suschestvovanie, Nauka, M., 1976 | MR

[12] Svirezhev Yu. M., Logofet D. O., Ustoichivost biologicheskikh soobschestv, Nauka, M., 1978 | MR

[13] Poluektov R. A., Pykh Yu. A., Shvytov I. A., Dinamicheskie modeli ekologicheskikh sistem, Gidrometeoizdat, L., 1980

[14] Khmelevskii Yu. I., Samovosproizvodyaschiesya sistemy. Matematicheskaya teoriya, Nauka, M., 1991 | MR

[15] Zubov V. I., “Differentsialnye uravneniya evolyutsii vidov”, Dokl. AN SSSR, 322:3 (1992), 456–459 | MR | Zbl

[16] Pertsev N. V., “O resheniyakh modeli Lotki–Volterra, uchityvayuschei ogranichennost vremeni zhizni osobei konkuriruyuschikh populyatsii”, Differents. uravneniya, 35:9 (1999), 1187–1193 | MR | Zbl

[17] Pertsev N. V., “Issledovanie reshenii integralnoi modeli Lotki–Volterra”, Sib. zhurn. industr. matematiki, 2:2(4) (1999), 153–167 | MR | Zbl

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

[19] M. A. Krasnoselskii, G. M. Vainiko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko (red.), Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR

[20] Kharris T., Teoriya vetvyaschikhsya sluchainykh protsessov, Mir, M., 1966

[21] Pichugina A. N., “Povedenie reshenii nelineinoi modeli Sharpa–Lotki”, Sib. zhurn. industr. matematiki, 5:3(11) (2002), 146–154 | MR | Zbl