Geodesic
The autoresonance threshold in a system of weakly coupled oscillators
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 43-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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A system of two weakly coupled oscillators is investigated. It is shown that under an external periodic perturbation a capture into resonance may occur. A description of this effect by the methods of asymptotic analysis, as well as a numerical simulation, is presented. An explicit formula for the threshold value of the perturbation amplitude at which the resonance occurs is obtained. 
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S. G. Glebov; O. M. Kiselev; V. A. Lazarev. The autoresonance threshold in a system of weakly coupled oscillators. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 43-54. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a3/

[1] McMillan E. M., “The synchrotron-a proposed high energy particle accelerator”, Phys. Rev., 68 (1945), 143 | DOI

[2] Veksler V. I., “Novyi metod uskoreniya relyativistskikh chastits”, Dokl. AN SSSR, 43:8 (1944), 346–348

[3] Veksler V. I., “O novom metode uskoreniya relyativistskikh chastits”, Dokl. AN SSSR, 44:9 (1944), 393–396

[4] Meerson B. , Friedland L., “Strong autoresonance excitation of Rydberg atoms: the Rydberg accelerator”, Phys. Rev. A, 41 (1990), 5233–5236 | DOI

[5] Meerson B. and Yariv S., “A rigid rotator under slowly-varying kicks: dynamic autoresonance and time-varying chaos”, Phys. Rev. A, 44 (1991), 3570–3582 | DOI

[6] Cohen G., Meerson B., “Dynamic autoresonance and global chaos in a slowly evolving system of two coupled oscillators”, Phys. Rev. E, 47:2 (1993), 967–975 | DOI

[7] Friedland L., “Autoresonant solutions of nonlinear Schrödinger equation”, Phys. Rev. E, 58 (1998), 3865–3875 | DOI | MR

[8] Friedland L., “Subharmonic autoresonance of the diocotron mode”, Physics of Plasmas, 7:5 (2000), 1712–1718 | DOI | MR

[9] Friedland L., “Subharmonic autoresonance”, Phys. Rev. E, 61:4 (2000), 3732–3735 | DOI | MR

[10] Kalyakin L. A., “Asimptoticheskii analiz modeli avtorezonansa”, Dokl. RAN., 378:5 (2001), 594–597 | MR | Zbl

[11] Kalyakin L. A., “Asimptoticheskoe reshenie zadachi o porogovom effekte dlya uravnenii glavnogo rezonansa”, Differents. uravneniya, 40:6 (2004), 731–739 | MR | Zbl

[12] Kalyakin L. A., “Rezonansnyi zakhvat v nelineinoi sisteme”, Teor. i mat. fizika, 144:1 (2005), 74–82 | MR

[13] Kozlov V. V., Furta S. D., Asimptotiki reshenii silno nelineinykh sistem differentsialnykh uravnenii, MGU, M., 1966, 244 pp. | MR

[14] Bryuno A. D., Stepennaya geometriya v algebraicheskikh i differentsialnykh uravneniyakh, Fizmatlit, M., 1998, 288 pp. | MR | Zbl

[15] Kuznetsov A. N., “Differentsiruemye resheniya vyrozhdayuschikhsya sistem obyknovennykh uravnenii”, Funkts. analiz i ego prilozheniya, 6:2 (1972), 41–51 | MR | Zbl

[16] Kalyakin L. A., Bagderina Yu. Yu., “Asimptotika ogranichennykh na beskonechnosti reshenii uravnenii kvadratichnogo glavnogo rezonansa”, Mat. zametki, 78:1 (2005), 85–97 | MR | Zbl