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

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Kuptsov P. V., Kuznetsov S. P. Dynamics of model systems with discrete time driven by binary self-similar sequences. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 2, pp. 3-16. DOI: 10.18500/0869-6632-1997-5-2-3-16

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-1997-5-2-3-16

Dynamics of model systems with discrete time driven by binary self-similar sequences

Autors: 
Kuptsov Pavel Vladimirovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

The dynamics of the 1D walking particle and the mao with pitch—fork bifurcation is considered when these model systems are forced by the self—similar sequences of two symbols constructed in accordance with substitution (inflation) rules. All such sequences are found to be divided into three classes which correspond to qualitatively different sorts of observed dynamics. It is shown that the matrix 2x2 is associated with the binary self— similar sequence and the one of eigenvalues of this characteristic matrix determines the class to what respective sequence belongs.

Key words: 
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Acknowledgments: 
The authors are grateful to A.P. Kuznetsov for useful discussions. The work was supported by the RFBR (grant 97-02-16414).
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Received: 
21.03.1997
Accepted: 
18.05.1997
Published: 
17.07.1997
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