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

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Zhusubaliev Z. T., Emelyanova E. Y. On synchronization of quasi-periodic oscillation at C-bifurcations in a piecewise-linear nonautonomous dynamic system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 5, pp. 57-71. DOI: 10.18500/0869-6632-2000-8-5-57-71

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
534.1:621.376.54
DOI: 
10.18500/0869-6632-2000-8-5-57-71

On synchronization of quasi-periodic oscillation at C-bifurcations in a piecewise-linear nonautonomous dynamic system

Autors: 
Zhusubaliev Zhanybaj Tursunbaevich, Federal state budgetary educational institution of higher professional education "South-West state University"
Emelyanova Elena Yurevna, Kursk State University
Abstract: 

The behaviour is examined of a piecewise—linear dynamic system with external periodic force at C-bifurcations which is related to resonance cycles arising from synchronization of quasi—periodic oscillation. As example the dynamics of the system of automatic control with pulse-width modulation first kind is considered which is represented by а three—dimensional piecewise—linear nonautonomous dynamic system. It has been revealed that within the parameter plane there are domains of existence of resonance cycles on two—dimension thorus (domains of synchronization). These domains have specific shape similar to Arnold’s tongues, but differ from them essentially in their internal structural organization and bifurcation transitions which cannot be achieved in smooth dynamic systems in principle. A detailed analytical description of C—boundaries structure and bifurcation transitions within the synchronization domain is there in this paper.

Key words: 
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Received: 
31.03.2000
Accepted: 
30.08.2000
Published: 
07.02.2001
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