Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the v...

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Published inChinese physics B Vol. 22; no. 7; pp. 79 - 83
Main Authors Gholizade-Narm, Hossein, Azemi, Asad, Khademi, Morteza
Format Journal Article
LanguageEnglish
Published 01.07.2013
Subjects
Delay
Describing functions
Dynamical systems
Joining
Mathematical analysis
Mathematical models
Oscillators
Pol
Synchronism
Synchronization
van
同步频率
固有振动频率
延迟
描述函数法
相同步
耦合振荡器
Online AccessGet full text
ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/22/7/070502

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Summary:In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.
Bibliography:Hossein Gholizade-Narm , Asad Azemi, and Morteza Khademi a） Faculty of Electrical, Electronic ＆ Robotic Engineering, Shahrood University Technology, Shahrood, Iran a） College of Engineering, Penn State University, USA b） Faculty of Engineering, Ferdowsi University of Mashhad, Iran
In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.
van der Pol oscillator;delay coupling;phase synchronization;synchronization frequency
11-5639/O4
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/7/070502