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Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks
December  2015, 10(4): 787-807. doi: 10.3934/nhm.2015.10.787

## 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, South Korea 3 Department of Mathematical Sciences, Seoul National University, Seoul, 151-747

Received  September 2014 Revised  June 2015 Published  October 2015

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. Networks & Heterogeneous Media, 2015, 10 (4) : 787-807. doi: 10.3934/nhm.2015.10.787
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