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

For citation:

Kipchatov A. A., Koronovskii A. A. The subtle effects of the piece-wise -linear system self-similar behaviour near the line of the torus birth bifurcation. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 2, pp. 17-23. DOI: 10.18500/0869-6632-1997-5-2-17-23

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-1997-5-2-17-23

The subtle effects of the piece-wise -linear system self-similar behaviour near the line of the torus birth bifurcation

Autors: 
Kipchatov A. A., Saratov State University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Abstract: 

The piece—wise linear system with 1.5 degrees of freedom which is able to demonstrate the two—frequency dynamics without the external action has been investigated in this article. It has been shown that the behaviour of this system near the line of the torus birth bifurcation is self-similar and very complicated. The tongues of synchronisation converge to the line of the torus birth bifurcation. There are another lines of torus birth bifurcation оп the tongues of synchronisation. The intersection of these lines results in the birth of the new quasiperiodic oscillation types, and so on.

Key words: 
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Reference: 
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Received: 
18.02.1997
Accepted: 
28.03.1997
Published: 
17.07.1997
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