Geodesic
Dynamics of strongly coupled spatially distributed logistic equations with delay
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 610-620 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The dynamics of a system of two logistic delay equations with spatially distributed coupling is studied. The coupling coefficient is assumed to be sufficiently large. Special nonlinear systems of parabolic equations are constructed such that the behavior of their solutions is determined in the first approximation by the dynamical properties of the original system. 
@article{ZVMMF_2015_55_4_a8,
     author = {I. S. Kashchenko and S. A. Kashchenko},
     title = {Dynamics of strongly coupled spatially distributed logistic equations with delay},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {610--620},
     year = {2015},
     volume = {55},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a8/}
}
TY  - JOUR
AU  - I. S. Kashchenko
AU  - S. A. Kashchenko
TI  - Dynamics of strongly coupled spatially distributed logistic equations with delay
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 610
EP  - 620
VL  - 55
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a8/
LA  - ru
ID  - ZVMMF_2015_55_4_a8
ER  - 
%0 Journal Article
%A I. S. Kashchenko
%A S. A. Kashchenko
%T Dynamics of strongly coupled spatially distributed logistic equations with delay
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 610-620
%V 55
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a8/
%G ru
%F ZVMMF_2015_55_4_a8
I. S. Kashchenko; S. A. Kashchenko. Dynamics of strongly coupled spatially distributed logistic equations with delay. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 610-620. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a8/

[1] Kuramoto Y., Battogtokh D., “Coexisting of coherence and incoherence in nonlocally coupled phase oscillators”, Nonlinear Phenomena in Complex Systems, 5:4 (2002), 380–385

[2] Wu J., Theory and applications of partial functional differential equations, Springer, 1996 | MR | Zbl

[3] Diekmann O., van Gils S. A., Verduyn Lunel S. M., Walther H.-O., Delay equation: functional-, complex- and nonlinear analysis, Springer, New York, 1995 | MR

[4] Kaschenko I. S., Kaschenko S. A., “Korporativnaya dinamika silno svyazannykh raspredelennykh sistem”, Dokl. AN, 442:5 (2012), 600–604 | Zbl

[5] Kaschenko S. A., “O kvazinormalnykh formakh dlya parabolicheskikh uravnenii s maloi diffuziei”, Dokl. AN SSSR, 299:5 (1988), 1049–1053

[6] Kaschenko I. S., Kaschenko S. A., “Dinamika uravneniya s bolshim prostranstvenno-raspredelennym upravleniem”, Dokl. AN, 438:1 (2011), 30–34 | Zbl

[7] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984 | MR

[8] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR

[9] Bryuno A. D., Lokalnyi metod nelineinogo analiza differentsialnykh uravnenii, Nauka, M., 1979 | MR

[10] Kaschenko I. S., “Asimptoticheskii analiz povedeniya reshenii uravneniya s bolshim zapazdyvaniem”, Dokl. AN, 421:5 (2008), 586–589 | Zbl

[11] Kaschenko S. A., “Dinamika prostranstvenno-raspredelennogo logisticheskogo uravneniya s maloi diffuziei i malym zapazdyvaniem”, Differents. ur-niya, 49:12 (2013), 1–10