Geodesic
Dynamic properties of first-order equations with large delay
Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 2, pp. 58-62.

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

The local dynamic of the first-order differential equation with large delay is studied. The method of research is based on the normal forms theory. In critical cases having infinite dimensions, special evolutional equations playing the role of normal form are built. Different cases of correlation between the order of coefficient variance from critical values and order of delay are studied. 
@article{MAIS_2007_14_2_a12,
     author = {I. S. Kashchenko},
     title = {Dynamic properties of first-order equations with large delay},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {58--62},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a12/}
}
TY  - JOUR
AU  - I. S. Kashchenko
TI  - Dynamic properties of first-order equations with large delay
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2007
SP  - 58
EP  - 62
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a12/
LA  - ru
ID  - MAIS_2007_14_2_a12
ER  - 
%0 Journal Article
%A I. S. Kashchenko
%T Dynamic properties of first-order equations with large delay
%J Modelirovanie i analiz informacionnyh sistem
%D 2007
%P 58-62
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a12/
%G ru
%F MAIS_2007_14_2_a12
I. S. Kashchenko. Dynamic properties of first-order equations with large delay. Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 2, pp. 58-62. http://geodesic.mathdoc.fr/item/MAIS_2007_14_2_a12/

[1] P. S. Landa, Avtokolebaniya v raspredelennykh sistemakh, Nauka, M., 1983, 320 pp. | MR | Zbl

[2] A. S. Dmitriev, V. Ya. Kislov, Stokhasticheskie kolebaniya v radiofizike i elektronike, Nauka, M., 1989, 280 pp. | MR | Zbl

[3] S. P. Kuznetsov, “Slozhnaya dinamika generatorov s zapazdyvayuschei obratnoi svyazyu (obzor)”, Izv. vuzov. Radiofizika, 25:12 (1982), 1410–1428

[4] T. Kilias, K. Kutzer, A. Moegel, W. Schwarz, “Electronic chaos generators – design and applications”, International Journal of Electronics, 79:6 (1995), 737–753 | DOI

[5] Dzh. Kheil, Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984, 421 pp. | MR

[6] S. A. Kaschenko, “Primenenie metoda normalizatsii k izucheniyu dinamiki differentsialno-raznostnykh uravnenii s malym mnozhitelem pri proizvodnoi”, Differentsialnye uravneniya, 25:8 (1989), 1448–1451 | MR

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

[8] V. I. Arnold, Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978, 304 pp. | MR