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Kiveleva K. G., Frajman L. A. The bifurcation analysis of nonautonomous pendulum equation from the theory of phase-locked loop. Izvestiya VUZ. Applied Nonlinear Dynamics, 1994, vol. 2, iss. 2, pp. 27-35.

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

The bifurcation analysis of nonautonomous pendulum equation from the theory of phase-locked loop

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 periodic solutions and homoclynic structures in nonautonomous system of differential equations which models phase—locked loop (PLL) is carried out with the qualitative numerical method using computer modelling. The chao tization of dynamics of the system is investigated. The bifurcation diagrams on the parameter plane with regions corresponding to different qualitative dynamics are presented. The achieved results are interpreted applying to PLL.

Key words: 
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Acknowledgments: 
The authors are grateful to V.N. Belykh for his attention and assistance in the work. The work was carried out with financial support from the Russian Foundation for Basic Research (project 93-013-16253).
Reference: 
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Received: 
29.04.1994
Accepted: 
12.07.1994
Published: 
08.08.1994
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