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Kuznetsov A. P., Turukina L. V. Dynamical systems of different classes as models of the kicked non-linear oscillator. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 2, pp. 31-42.

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9

Dynamical systems of different classes as models of the kicked non-linear oscillator

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Turukina L. V., Saratov State University
Abstract: 

Correspondence between the models as dynamical systems of different classes is discussed by the example of nonlinear dissipative kicked oscillator. 1D map is investigated in details: Feigenbaum’s period doubling is studied and the possibility of non—Feigenbaum’s period doubling is shown, corresponding illustration in the form of bifurcation diagrams and set of iteration diagrams are given, tricritical points (terminal points of the Feigenbaum’s critical curves) are found in parameter space. The correlation with the properties of 2D map, the phenomenon of tricritically dynamics was demonstrated to take place only on definite areas of the parameter space.

Key words: 
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Acknowledgments: 
The authors would like to thank S.P. Kuznetsov for fruitful discussion of the article. The work was supported by the RFBR (grant № 97-02-16414), Federal Target Program "Integration" (grant № 696.3) and Ministry of Education of the Russian Federation (grant № 97-0-8.3-88).
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Received: 
25.09.1999
Accepted: 
24.01.2000
Published: 
25.05.2000
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