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Dependence of synchronization frequency of Kuramoto oscillators on symmetry of intrinsic frequency in ring network

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Abstract

Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronization. In this article, we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We first indicate that synchronization frequency of oscillators in a completely connected network is always equal to the mean of the natural frequency distribution. In particular, shape of the natural frequency distribution does not affect the synchronization frequency in this case. Then, we analyse the case of oscillators in a directed ring network, where asymmetry in the natural frequency distribution is seen to shift the synchronization frequency of the network. We also present an estimate of the shift in the frequencies for slightly asymmetric distributions.

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Authors and Affiliations

  1. Department of Physical Sciences, Indian Institute of Science Education and Research, Kolkata, 741 252, India

    ARINDAM SAHA

  2. Department of Theoretical Physics, Physical Research Laboratory, Ahmedabad, 380 009, India

    R E AMRITKAR

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  1. ARINDAM SAHA
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  2. R E AMRITKAR
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Correspondence to ARINDAM SAHA.

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SAHA, A., AMRITKAR, R.E. Dependence of synchronization frequency of Kuramoto oscillators on symmetry of intrinsic frequency in ring network. Pramana - J Phys 83, 945–953 (2014). https://doi.org/10.1007/s12043-014-0831-5

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  • DOI: https://doi.org/10.1007/s12043-014-0831-5

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