On the sequence of period doubling bifurcations in Rossler models
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 96-103 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Bogolyubov's asymptotic methods are used to develop an approach to find relations in the space of parameters of the system that determine the sequence of period doubling bifurcations in dynamical models of Rossler type. A distribution law is found, and the existence of a limit set of bifurcation values of the parameters is demonstrated.
@article{TMF_1991_88_1_a12,
     author = {V. V. Alekseev and M. Kh. Kharrasov},
     title = {On the sequence of period doubling bifurcations in {Rossler} models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {96--103},
     year = {1991},
     volume = {88},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a12/}
}
TY  - JOUR
AU  - V. V. Alekseev
AU  - M. Kh. Kharrasov
TI  - On the sequence of period doubling bifurcations in Rossler models
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1991
SP  - 96
EP  - 103
VL  - 88
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a12/
LA  - ru
ID  - TMF_1991_88_1_a12
ER  - 
%0 Journal Article
%A V. V. Alekseev
%A M. Kh. Kharrasov
%T On the sequence of period doubling bifurcations in Rossler models
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 96-103
%V 88
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a12/
%G ru
%F TMF_1991_88_1_a12
V. V. Alekseev; M. Kh. Kharrasov. On the sequence of period doubling bifurcations in Rossler models. Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 96-103. http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a12/

[1] Goponov-Grekhov A. V., Rabinovich M. I., “Nelineinaya fizika. Stokhastichnost i struktury”, Fizika XX veka. Razvitie i perspektivy, Nauka, M., 1985

[2] Khaken G., Sinergetika, Mir, M., 1985 | MR

[3] Zaslavskii G. M., Sagdeev R. Z., Vvedenie v nelineinuyu fiziku, Nauka, M., 1988 | MR

[4] Svirezhev Yu. M., Nelineinye volny. Dissipativnye struktury i katastrofy v ekologii, Nauka, M., 1987 | MR | Zbl

[5] Alekseev V. V., Loskutov A. Yu., DAN SSSR, 239:6 (1987), 1346–1348 | MR

[6] Feigenbaum M., J. Stat. Phys., 19:1 (1978), 25–52 | DOI | MR | Zbl

[7] Ott E., Rev. Mod. Phys., 53:4 (1981), 655–671 | DOI | MR | Zbl

[8] Alekseev V. V., Kornilovsky A. N., Ecol. Mod., 28 (1985), 217–219 | DOI

[9] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[10] Rossler O. E., “Chaos and Strange Attractor in Chemical Kinetics”, Springer Serie in Synergetics, 3, 1979, 103–113 | MR

[11] Butenin N. V., Neimark Yu. M., Fufaev N. A., Vvedenie v teoriyu nelineinykh kolebanii, Nauka, M., 1987 | MR | Zbl