Parametric excitation of chaotic oscillations in one second order differential equation with delay
Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 67-71.

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We study some differential equations with delay that are the models of different electronic devices. We show that the internal resonance is a reason why the regions associated with chaotic oscillations appear in the parametric resonance domain. The scenario of the chaotic oscillations emergence is studied. We calculate Lyapunov exponents and Lyapunov dimension of the chaotic attractor.
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E. P. Kubishkin; A. Yu. Koverga. Parametric excitation of chaotic oscillations in one second order differential equation with delay. Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 2, pp. 67-71. http://geodesic.mathdoc.fr/item/MAIS_2008_15_2_a10/

[1] V. P. Rubanik, Kolebaniya kvazilineinykh sistem s zapazdyvaniem, Nauka, M., 1969, 288 pp. | MR | Zbl

[2] M. V. Kapranov, V. N. Kuleshov, G. M. Utkin, Teoriya kolebanii v radiotekhnike, Nauka, M., 1984, 320 pp.

[3] S. D. Glyzin, E. P. Kubyshkin, “Nelineinaya dinamika odnogo differentsialnogo uravneniya vtorogo poryadka s periodicheski vozmuschennym zapazdyvaniem”, Modelirovanie i analiz informatsionnykh sistem, 12:1 (2005), 40–45 | MR

[4] Yu. S. Kolesov, D. I. Shvitra, Avtokolebaniya v sistemakh s zapazdyvaniem, Mokslas, Vilnyus, 1979, 148 pp. | MR | Zbl

[5] E. P. Kubyshkin, “Parametricheskii rezonans v lineinykh periodicheskikh sistemakh s posledeistviem”, Issledovaniya po ustoichivosti i teorii kolebanii, Yaroslavl, 1978, 43–76 | MR | Zbl

[6] D. Khenri, Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Nauka, M., 1985, 376 pp. | MR