Local dynamics of an equation with long delay feedback
Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 1, pp. 75-85.

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

We study the local dynamics of a nonlinear complex DDE with large delay in the vicinity of the zero solution. The quasinormal forms method is used for the problem analysis. We show that parabolic type GL-equations act as normal forms in critical cases of the infinite dimension.
Keywords: delay; laser model; normal form; asymptotic formula; small parameter.
@article{MAIS_2011_18_1_a7,
     author = {D. V. Glazkov},
     title = {Local dynamics of an equation with long delay feedback},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {75--85},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a7/}
}
TY  - JOUR
AU  - D. V. Glazkov
TI  - Local dynamics of an equation with long delay feedback
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2011
SP  - 75
EP  - 85
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a7/
LA  - ru
ID  - MAIS_2011_18_1_a7
ER  - 
%0 Journal Article
%A D. V. Glazkov
%T Local dynamics of an equation with long delay feedback
%J Modelirovanie i analiz informacionnyh sistem
%D 2011
%P 75-85
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a7/
%G ru
%F MAIS_2011_18_1_a7
D. V. Glazkov. Local dynamics of an equation with long delay feedback. Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 1, pp. 75-85. http://geodesic.mathdoc.fr/item/MAIS_2011_18_1_a7/

[1] S. Schikora et al., “All-Optical Noninvasive Control of Unstable Steady States in a Semiconductor Laser”, Phys. Rev. Lett., 97 (2006), 213902 | DOI

[2] D. V. Glazkov, “Osobennosti dinamiki modeli Langa-Kobayashi v odnom kriticheskom sluchae”, Modelirovanie i analiz informatsionnykh sistem, 15:2 (2008), 36–45 | MR

[3] P. Hövel, E. Schöll, “Control of unstable steady states by time-delayed feedback methods”, Phys. Rev. E, 72 (2005), 046203 | DOI

[4] S. et al. Yanchuk, “Control of unstable steady states by long delay feedback”, Phys. Rev. E, 74 (2006), 026201 | DOI | MR

[5] L. E. Elsgolts, S. B. Norkin, Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1971, 296 pp. | MR

[6] S. A. Kaschenko, “Primenenie metoda normalizatsii k izucheniyu dinamiki differentsialno-raznostnykh uravnenii s malym mnozhitelem pri proizvodnoi”, Differentsialnye uravneniya, 25:2 (1989), 262–270 | MR

[7] S. A. Kaschenko, “Lokalnaya dinamika nelineinykh singulyarno vozmuschennykh sistem s zapazdyvaniem”, Differentsialnye uravneniya, 35:10 (1999), 1343–1355 | MR

[8] D. S. Kaschenko, I. S. Kaschenko, Dinamika uravnenii pervogo poryadka s zapazdyvaniem, YarGU, Yaroslavl, 2006, 132 pp.

[9] A. Yu. Kolesov, E. F. Mischenko, N. Kh. Rozov, “Novye metody dokazatelstva suschestvovaniya i ustoichivosti periodicheskikh reshenii v singulyarno vozmuschennykh sistemakh s zapazdyvaniem”, Tr. MIAN, 259, 2007, 106–133 | MR | Zbl