Geodesic
Resonance Dynamics of Nonlinear Flutter Systems
Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 154-175.

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

We consider a special class of nonlinear systems of ordinary differential equations, namely, the so-called flutter systems, which arise in Galerkin approximations of certain boundary value problems of nonlinear aeroelasticity and in a number of radiophysical applications. Under the assumption of small damping coefficient, we study the attractors of a flutter system that arise in a small neighborhood of the zero equilibrium state as a result of interaction between the $1:1$ and $1:2$ resonances. We find that, first, these attractors may be both regular and chaotic (in the latter case, we naturally deal with numerical results); and second, for certain parameter values, they coexist with the stable zero solution; i.e., the phenomenon of hard excitation of self-oscillations is observed. 
@article{TRSPY_2008_261_a11,
     author = {A. Yu. Kolesov and E. F. Mishchenko and N. Kh. Rozov},
     title = {Resonance {Dynamics} of {Nonlinear} {Flutter} {Systems}},
     journal = {Informatics and Automation},
     pages = {154--175},
     publisher = {mathdoc},
     volume = {261},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a11/}
}
TY  - JOUR
AU  - A. Yu. Kolesov
AU  - E. F. Mishchenko
AU  - N. Kh. Rozov
TI  - Resonance Dynamics of Nonlinear Flutter Systems
JO  - Informatics and Automation
PY  - 2008
SP  - 154
EP  - 175
VL  - 261
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a11/
LA  - ru
ID  - TRSPY_2008_261_a11
ER  - 
%0 Journal Article
%A A. Yu. Kolesov
%A E. F. Mishchenko
%A N. Kh. Rozov
%T Resonance Dynamics of Nonlinear Flutter Systems
%J Informatics and Automation
%D 2008
%P 154-175
%V 261
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a11/
%G ru
%F TRSPY_2008_261_a11
A. Yu. Kolesov; E. F. Mishchenko; N. Kh. Rozov. Resonance Dynamics of Nonlinear Flutter Systems. Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 154-175. http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a11/

[1] Bolotin V. V., Nekonservativnye zadachi teorii uprugoi ustoichivosti, Fizmatgiz, M., 1961 | MR

[2] Khessard B., Kazarinov N., Ven I., Teoriya i prilozheniya bifurkatsii rozhdeniya tsikla, Mir, M., 1985 | MR

[3] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie sistemy i bifurkatsii vektornykh polei, In-t kompyut. issled., M., Izhevsk, 2002

[4] Kulikov A. N., “Nelineinyi panelnyi flatter: opasnost zhestkogo vozbuzhdeniya kolebanii”, Dif. uravneniya, 28:6 (1992), 1080–1082 | MR | Zbl

[5] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., Asimptoticheskie metody issledovaniya periodicheskikh reshenii nelineinykh giperbolicheskikh uravnenii, Tr. MIAN, 222, Nauka, M., 1998 | MR | Zbl

[6] Kolesov A. Yu., Rozov N. Kh., “Yavlenie bufernosti v $RCLG$-avtogeneratore: teoreticheskii analiz i rezultaty eksperimenta”, Tr. MIAN, 233, 2001, 153–207 | MR | Zbl

[7] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Mekhanizm zhestkogo vozbuzhdeniya avtokolebanii, svyazannyi s rezonansom $1:2$”, ZhVMiMF, 45:11 (2005), 2000–2016 | MR | Zbl

[8] http://tracer3.narod.ru

[9] Kuznetsov S. P., Dinamicheskii khaos: Kurs lektsii, Fizmatlit, M., 2001

[10] Dmitriev A. S., Panas A. I., Dinamicheskii khaos: novye nositeli informatsii dlya sistem svyazi, Fizmatlit, M., 2002

[11] Kolesov A. Yu., Rozov N. Kh., “O prirode yavleniya bufernosti v slabo dissipativnykh sistemakh”, TMF, 146:3 (2006), 447–466 | MR | Zbl