中国物理B ›› 2013, Vol. 22 ›› Issue (7): 70502-070502.doi: 10.1088/1674-1056/22/7/070502

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

Hossein Gholizade-Narma, Asad Azemib, Morteza Khademic   

  1. 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
  • 收稿日期:2012-08-08 修回日期:2013-01-09 出版日期:2013-06-01 发布日期:2013-06-01

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

Hossein Gholizade-Narma, Asad Azemib, Morteza Khademic   

  1. a Faculty of Electrical, Electronic & Robotic Engineering, Shahrood University Technology, Shahrood, Iran b  College of Engineering, Penn State University, USA;
    c Faculty of Engineering, Ferdowsi University of Mashhad, Iran
  • Received:2012-08-08 Revised:2013-01-09 Online:2013-06-01 Published:2013-06-01
  • Contact: Hossein Gholizade-Narm E-mail:h_gholizade@yahoo.com

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摘要： 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.

关键词: van der Pol oscillator, delay coupling, phase synchronization, synchronization frequency

Abstract: 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.

Key words: van der Pol oscillator, delay coupling, phase synchronization, synchronization frequency

中图分类号:  (Synchronization; coupled oscillators)

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