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Kiveleva K. G., Frajman L. A. The bifurcation analysis of nonlinear dynamics in nonautonomous pendulum system. Izvestiya VUZ. Applied Nonlinear Dynamics, 1996, vol. 4, iss. 4, pp. 13-20.

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
531.01

The bifurcation analysis of nonlinear dynamics in nonautonomous pendulum system

Autors: 
Kiveleva Klara Georgievna, Institute of Applied Mathematics and Cybernetics. Nizhny Novgorod state University
Frajman Ljudmila Alekseevna, Institute of Applied Mathematics and Cybernetics. Nizhny Novgorod state University
Abstract: 

The bifurcation analysis of nonlinear dynamics in nonautonomous pendulum systems with extensive spectrum of applications is carried out. The bifurcation diagrams are presented, the regions with chaotic motions of different types are determined, the case of appearance of two stable oscillating periodic solutions is studied. The achieved results are interpreted applying to Josephson junction systems.

Key words: 
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Acknowledgments: 
The authors are grateful to V.N. Belykh for useful discussions during the research and comments on the work. The work was carried out with partial financial support from the Russian Foundation for Basic Research (grant N 93-13-16253).
Reference: 
  1. Kiveleva КG, Fraiman LА. Bifurcation analysis of a non-autonomous pendulum equation from the theory of phase synchronisation systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(2):27-35.
  2. Stoker JJ. Nonlinear Vibrations in Mechanical and Electrical Systems. N.Y.: Wiley; 1992. 296 p.
  3. Likharev KK. Systems with Josephson contacts. M.: Moscow University Press; 1978. 446 p.
  4. Nesvizhskii OV. Forced fluctuations in the phase automatic frequency adjustment system. Radio engineering. 1965;20:7.
  5. Belyustina LN. Study of some nonlinear non-autonomous systems of the second order by qualitative numerical methods. In: Stability Theory and Its Applications. Novosibirsk: Nauka; 1979. P.339.
  6. Shakhgildyan VV, Belyustina LN. Phase Synchronization Systems. М.: Radio i svyaz; 1975. 288 p. (in Russian).
Received: 
31.05.1995
Accepted: 
17.06.1996
Published: 
10.12.1996
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