Geodesic
The Buffer Phenomenon in second-order equations with large delay
Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 31-35.

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

Local dynamics of second-order differential equation with large delay is studied. The research method uses normal forms technique. In critical cases of infinite dimension special evolutional equations playing the role of normal forms are built. We prove that such equations may have any number of stable periodic solutions. Some numerical results are provided. 
@article{MAIS_2008_15_2_a4,
     author = {I. S. Kashchenko},
     title = {The {Buffer} {Phenomenon} in second-order equations with large delay},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {31--35},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a4/}
}
TY  - JOUR
AU  - I. S. Kashchenko
TI  - The Buffer Phenomenon in second-order equations with large delay
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2008
SP  - 31
EP  - 35
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a4/
LA  - ru
ID  - MAIS_2008_15_2_a4
ER  - 
%0 Journal Article
%A I. S. Kashchenko
%T The Buffer Phenomenon in second-order equations with large delay
%J Modelirovanie i analiz informacionnyh sistem
%D 2008
%P 31-35
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a4/
%G ru
%F MAIS_2008_15_2_a4
I. S. Kashchenko. The Buffer Phenomenon in second-order equations with large delay. Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 31-35. http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a4/

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

[2] A. S. Dmitriev, V. Ya. Kislov, Stokhasticheskie kolebaniya v radiofizike i elektronike, Nauka, M., 1989 | 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, “Electromic chaos generators — design and applications”, International Journal of Electronics, 79:6 (1995), 737–753 | DOI

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

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

[7] S. A. Kaschenko, “Uravneniya Ginzburga-Landau — normalnaya forma dlya differentsialno-raznostnogo uravneniya vtorogo poryadka s bolshim zapazdyvaniem”, Zhurnal Vychisl. matem. i matem. fiz., 38:3 (1998), 457–465 | MR

[8] I. S. Kaschenko, “Dinamicheskie svoistva uravnenii pervogo poryadka s bolshim zapazdyvaniem”, Modelirovanie i analiz informatsionnykh sistem, 14:2 (2007), 58–62

[9] A. Yu. Kolesov, N. Kh. Rozov, Invariantnye tory nelineinykh volnovykh uravnenii, FIZMATLIT, M., 1994

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