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

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Kuznetsov A. P., Potapova A. Y. A features of the complex dynamics of the nonlinear oscillators with Thom’s catastrophes. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 6, pp. 94-120. DOI: 10.18500/0869-6632-2000-8-6-94-120

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Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2000-8-6-94-120

A features of the complex dynamics of the nonlinear oscillators with Thom’s catastrophes

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Potapova Anna Yurevna, Saratov State University
Abstract: 

A survey of the regular and chaotic phenomena in the periodically forced nonlinear oscillators is represented. To classify the nonlinear oscillators the scheme of the catastrophe theory is used. Developed classification allows to describe the dynamics of ° many physical systems, which differ each from others in both the quantity of the potential wells and the possibility to escape from them, by using the only oscillator equation with some appropriate Thom's catastrophe as the potential function. The escape region and the region of the non-escaping solutions are estimated on the plane of the nonlinear parameter and forcing amplitudes for the oscillator with fold catastrophe. The boundary between these regions is illustrated by the basin erosion sequence. The dynamical regimes topographies which contain а crossroad area and а spring area are shown for the oscillators with high degree polynomial potential function. General features of topographies evolution for the oscillators with cusp catastrophe and with butterfly catastrophe are described. The bifurcations and crises, which occur in the considered systems, also depend on the degree of the potential function.

Key words: 
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Acknowledgments: 
The work was supported by the Ministry of Education of the Russian Federation (grant № 00-02-17509) and CRDF REC-006.
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Received: 
23.10.2000
Accepted: 
14.12.2000
Published: 
25.03.2001
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