Networks and Heterogeneous Media (NHM)

Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics

Pages: 787 - 807, Volume 10, Issue 4, December 2015      doi:10.3934/nhm.2015.10.787

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Seung-Yeal Ha - Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, South Korea (email)
Se Eun Noh - Department of Mathematics, Myongji University, Yong-In, 449-728, South Korea (email)
Jinyeong Park - Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, South Korea (email)

Abstract: 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.

Keywords:  Kuramoto model, intrinsic dynamics, external force, practical synchronization.
Mathematics Subject Classification:  Primary: 70F99; Secondary: 92B25.

Received: September 2014;      Revised: June 2015;      Available Online: October 2015.