ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Seleznev E. P., Zaharevich A. M. Control parameter space of a nonlinear oscillator under quasiperiodic driving. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 6, pp. 17-35. DOI: 10.18500/0869-6632-2009-17-6-17-35

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
518.30
DOI: 
10.18500/0869-6632-2009-17-6-17-35

Control parameter space of a nonlinear oscillator under quasiperiodic driving

Autors: 
Seleznev Evgeny Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Zaharevich Andrej Mihajlovich, Saratov State University
Abstract: 

Dynamics and space of сontrol parameters for a nonlinear oscillator under quasi­periodic driving are investigated experimentally by using a nonlinear circuit with p­n junction diode and numerically by using maps and differential equations. The dynamics of the systems under quasiperiodic driving is invariant due to initial driving phases, as a result the plane of the driving amplitudes is symmetrical. The basic element of the control parameter space is the set of torus doubling terminal points, which are the starting and end points of the torus doubling lines, transition to strange non­chaotic and chaotic attractors.

Key words: 
Strange nonchaotic attractor
torus doubling
torus doubling terminal point
singular continuous spectrum
rational approximation method
phase sensitivity method
Lyapunov exponent
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Received: 
12.05.2008
Accepted: 
07.07.2009
Published: 
31.12.2009
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