Geodesic
On global behaviour of the solutions of system of two Duffing -- Van der Pole equations
Russian journal of nonlinear dynamics, Tome 7 (2011) no. 3, pp. 437-449.

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The problem of global behavior of solutions in system of two Duffing – Van der Pole equations close to nonlinear integrable is considered. For regions without unperturbed separatrixes we give partially averaged systems which describe the behavior of solutions of original system in resonant zones. The finiteness of number of non-trivial resonant structures is established. Also we give fully averaged systems which describe the behavior of solutions outside of neighborhoods of nontrivial resonant structures. The results of numerically investigation of these systems are resulted.
Mots-clés : limit cycles
Keywords: resonances, averaging. 
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R. E. Kondrashov; A. D. Morozov. On global behaviour of the solutions of system of two Duffing -- Van der Pole equations. Russian journal of nonlinear dynamics, Tome 7 (2011) no. 3, pp. 437-449. http://geodesic.mathdoc.fr/item/ND_2011_7_3_a2/

[1] Andronov A. A., Vitt A. A., “K teorii zakhvatyvaniya Van der Polya”, Sobr. tr. A. A. Andronova, AN SSSR, M., 1956, 51–64

[2] Butenin N. V., Neimark Yu. I., Fufaev N. A., Vvedenie v teoriyu nelineinykh kolebanii, Nauka, M., 1976, 384 pp.

[3] Morozov A. D., Shilnikov L. P., “O nekonservativnykh periodicheskikh sistemakh, blizkikh k dvumernym gamiltonovym”, PMM, 47:3 (1983), 385–394 | MR

[4] Morozov A. D., Rezonansy, tsikly i khaos v kvazikonservativnykh sistemakh, NITs «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2005, 420 pp.

[5] Morozov A. D., Kondrashov R. E., “On resonances in systems of two weakly connected oscillators”, Regul. Chaotic Dyn., 14:2 (2009), 237–247 | DOI | MR

[6] Kondrashov R. E., Morozov A. D., “K issledovaniyu rezonansov v sisteme dvukh uravnenii Dyuffinga – Van der Polya”, Nelineinaya dinamika, 6:2 (2010), 241–254

[7] Belykh V. N., Pankratova E. V., “Chaotic dynamics of two Van der Pol – Duffing oscillators with huygens coupling”, Regul. Chaotic Dyn., 15:2–3 (2010), 274–284 | DOI | MR | Zbl

[8] Morozov A. D., “K issledovaniyu rezonansov v sisteme nelineinykh slabosvyazannykh ostsillyatorov”, Metody kachestvennoi teorii differentsialnykh uravnenii, Mezhvuz. temat. sb. nauchn. trudov, ed. E. A. Leontovich-Andronova, GGU, Gorkii, 1984, 147–158

[9] Karabanov A. A., Nekotorye aspekty rezonansnoi dinamiki chetyrekhmernykh kvazigamiltonovykh sistem, Nauchnye doklady, 415, Komi nauchnyi tsentr UrO RAN, Syktyvkar, 1999, 32 pp.

[10] Morozov A. D., Dragunov T. N., Vizualizatsiya i analiz invariantnykh mnozhestv dinamicheskikh sistem, Inst. kompyutern. issled., M.–Izhevsk, 2003, 304 pp.