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

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Balyakin A. A., Ryskin N. M. Peculiarities of calculation of the Lyapunov exponents set in distributed self-oscillated systems with delayed feedback. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 6, pp. 3-21. DOI: 10.18500/0869-6632-2007-15-6-3-21

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2007-15-6-3-21

Peculiarities of calculation of the Lyapunov exponents set in distributed self-oscillated systems with delayed feedback

Autors: 
Balyakin Artem Aleksandrovich, Saratov State University
Ryskin Nikita Mikhailovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

The numerical scheme for calculation the set of Lyapunov exponents in distributed systems with delayed feedback based on a modification of Benettine algorithm is described. The results of numerical simulation of two such systems (active oscillator with cubic nonlinearity and active oscillator of klystron type) are presented. The sets of Lyapunov exponents in different regimes, particularly in regimes of «weak» and «developed» chaos are analyzed. The calculation peculiarities of the set of Lyapunov exponents in the systems with delayed feedback are discussed.

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Received: 
07.05.2007
Accepted: 
07.09.2007
Published: 
30.01.2008
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