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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 6, Pages 129–152 (Mi izv608)  

Smoothing the discontinuous oscillations in the mathematical model of an oscillator with distributed parameters

A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We suggest a method of smoothing the discontinuous oscillations in mathematical models of oscillators with a long line segment in the feedback circuit. We show that under certain conditions the buffer phenomenon is realized in the corresponding boundary-value problem, that is, this problem can have a finite number of stable cycles (time-periodic solutions) as large as desired.

DOI: https://doi.org/10.4213/im608

Full text: PDF file (612 kB)
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English version:
Izvestiya: Mathematics, 2006, 70:6, 1201–1224

Bibliographic databases:

UDC: 517.926
MSC: 35B10, 35B25, 35B35, 35Q80, 35K50, 35K57, 35L75
Received: 10.03.2005
Revised: 19.06.2006

Citation: A. Yu. Kolesov, N. Kh. Rozov, “Smoothing the discontinuous oscillations in the mathematical model of an oscillator with distributed parameters”, Izv. RAN. Ser. Mat., 70:6 (2006), 129–152; Izv. Math., 70:6 (2006), 1201–1224

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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