Running Lyapunov exponents and the conditions for the occurrence of chaos
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 9, pp. 1409-1421 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_1992_32_9_a5,
     author = {D. M. Vavriv and V. B. Ryabov},
     title = {Running {Lyapunov} exponents and the conditions for the occurrence of chaos},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1409--1421},
     year = {1992},
     volume = {32},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_9_a5/}
}
TY  - JOUR
AU  - D. M. Vavriv
AU  - V. B. Ryabov
TI  - Running Lyapunov exponents and the conditions for the occurrence of chaos
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1992
SP  - 1409
EP  - 1421
VL  - 32
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_9_a5/
LA  - ru
ID  - ZVMMF_1992_32_9_a5
ER  - 
%0 Journal Article
%A D. M. Vavriv
%A V. B. Ryabov
%T Running Lyapunov exponents and the conditions for the occurrence of chaos
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1992
%P 1409-1421
%V 32
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_9_a5/
%G ru
%F ZVMMF_1992_32_9_a5
D. M. Vavriv; V. B. Ryabov. Running Lyapunov exponents and the conditions for the occurrence of chaos. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 9, pp. 1409-1421. http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_9_a5/

[1] Guckenheimer J., Holmes P., Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer, N. Y., 1983 | MR | Zbl

[2] Neimark Yu. I., Landa P. S., Stokhasticheskie i khaoticheskie kolebaniya, Nauka, M., 1987 | MR

[3] Parker T. S., Chua L. O., “Chaos: A tutorial for engineers”, Proc. IEEE, 75:8 (1987), 982–1008 | DOI

[4] Anischenko V. S., Slozhnye kolebaniya v prostykh sistemakh, Nauka, M., 1990 | MR

[5] Melnikov V. K., “Ustoichivost tsentra pri periodicheskikh vo vremeni vozmuscheniyakh”, Tr. Mosk. matem. ob-va, 12, no. 1, 1963, 3–52

[6] Wiggins S., Global bifurcations and chaos: Analytical methods, Springer, N. Y., 1987 | MR

[7] Yagasaki K., “Second order averaging and chaos in quasiperiodically forced weakly nonlinear oscillators”, Physica D, 44 (1990), 445–458 | DOI | MR | Zbl

[8] Ryabov V. B., Vavriv D. M., “Conditions of quasiperiodic oscillation destruction in the weakly nonlinear Duffing oscillator”, Phys. Letts. A, 153:8/9 (1991), 431–436 | DOI | MR

[9] Yakubovich V. A., Starzhinskii V. M., Lineinye differentsialnye uravneniya s periodicheskimi koeffitsientami i ikh prilozheniya, Nauka, M., 1972 | MR

[10] Herzel H., Schulmeister Th., “Chaotic dynamics and fluctuations in a biochemical system”, Dynamical Systems and Environmental Models, Akad.-Verl., Berlin, 1987 | MR

[11] Morita M., Hata H., Mori H. et al., “Local structures of chaotic attractors and $q$-phase transistions at attractor-merging crises in the Sine-circle map”, Progr. Theor. Phys., 80:5 (1988), 793–808 | DOI | MR

[12] Nicolis J. S., “Chaotic dynamics applied to information processing”, Rept. Progr. Phys., 49 (1986), 1109–1196 | DOI | MR

[13] Vavriv D. M., Ryabov V. B., “Tekuschie pokazateli Lyapunova”, Dokl. AN USSR. Ser. A, 1990, no. 2, 50–62 | MR

[14] Grassberger P., Procaccia I., “Dimensions and entropies of strange attractors from a fluctuating dynamics approach”, Physica D, 13:1/2 (1984), 34–54 | DOI | MR | Zbl

[15] Benettin G., Galgani L., Giorgilli A., Strelcyn J. M., “Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. 1; 2”, Meccanica, 15:1 (1980), 9–30 | DOI | MR

[16] Grassberger P., Badii R., Politi A., “Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors”, J. Statist. Phys., 51:1/2 (1988), 135–178 | DOI | MR | Zbl

[17] Belogortsev A. B., Vavriv D. M., Tretyakov O. A., “O vovlechenii passivnoi mody v turbulentnoe dvizhenie”, Zh. eksperim. i teor. fiz., 92:4 (1987), 1316–1321

[18] Miles J., “Chaotic motion of a weakly nonlinear, modulated oscillator”, Proc. Nat. Acad. Sci. USA: Phys. Sci., 81:12 (1984), 3919–3923 | DOI | MR | Zbl

[19] Vavriv D. M., Tretyakov O. A., Chernyshov I. Yu., “Razrushenie dvukhchastotnykh kolebanii v nelineinom konture”, Radiotekhn. i elektronika, 34:8 (1989), 1698–1706

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

[21] Likharev K. K., Vvedenie v dinamiku dzhozefsonovskikh perekhodov, Nauka, M., 1985

[22] Danilov V. V., Likharev K. K., “Dinamicheskie i fluktuatsionnye parametry radiochastotnykh skvidov”, Radiotekhn. i elektronika, 25:8 (1980), 1725–1735

[23] Danilov V. V., Likharev K. K., “Predelnye kharakteristiki sverkhprovodyaschego kvantovogo magnetometra”, Zh. tekhn. fiz., 45:5 (1975), 1110–1116

[24] Bulgakov S. A., Ryabov V. B., Shnyrkov V. I., Vavriv D. M., “Effect of the magnetic-flux variations on SQUID stability”, J. Low Temp. Phys., 83:5/6 (1991), 241–255 | DOI