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Networks and Heterogeneous Media

2015, Volume 10, Issue 4: 787-807. doi: 10.3934/nhm.2015.10.787
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Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics

  • 1.
    Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747
  • 2.
    Department of Mathematics, Myongji University, Yong-In, 449-728
  • 3.
    Department of Mathematical Sciences, Seoul National University, Seoul, 151-747
  • Received: 01 September 2014 Revised: 01 June 2015

  • Primary: 70F99; Secondary: 92B25.

  • We study the practical synchronization of the Kuramoto dynamics of units distributed over networks. The unit dynamics on the nodes of the network are governed by the interplay between their own intrinsic dynamics and Kuramoto coupling dynamics. We present two sufficient conditions for practical synchronization under homogeneous and heterogeneous forcing. For practical synchronization estimates, we employ the configuration diameter as a Lyapunov functional, and derive a Gronwall-type differential inequality for this value.

    Citation: Seung-Yeal Ha, Se Eun Noh, Jinyeong Park. Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics[J]. Networks and Heterogeneous Media, 2015, 10(4): 787-807. doi: 10.3934/nhm.2015.10.787

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  • We study the practical synchronization of the Kuramoto dynamics of units distributed over networks. The unit dynamics on the nodes of the network are governed by the interplay between their own intrinsic dynamics and Kuramoto coupling dynamics. We present two sufficient conditions for practical synchronization under homogeneous and heterogeneous forcing. For practical synchronization estimates, we employ the configuration diameter as a Lyapunov functional, and derive a Gronwall-type differential inequality for this value.


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