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Chin. Phys. B, 2019, Vol. 28(12): 120503    DOI: 10.1088/1674-1056/ab55d0
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Relaxation dynamics of Kuramoto model with heterogeneous coupling

Tianwen Pan(潘天文)1, Xia Huang(黄霞)2, Can Xu(徐灿)3, Huaping Lü(吕华平)1
1 School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China;
2 School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
3 Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
Abstract  The Landau damping which reveals the characteristic of relaxation dynamics for an equilibrium state is a universal concept in the area of complex system. In this paper, we study the Landau damping in the phase oscillator system by considering two types of coupling heterogeneity in the Kuramoto model. We show that the critical coupling strength for phase transition, which can be obtained analytically through the balanced integral equation, has the same formula for both cases. The Landau damping effects are further explained in the framework of Laplace transform, where the order parameters decay to zero in the long time limit.
Keywords:  synchronization      coupled oscillators      Landau damping  
Received:  07 October 2019      Revised:  28 October 2019      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
  68.18.Jk (Phase transitions in liquid thin films)  
  89.75.-k (Complex systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11905068, 11847013, 11175150, and 11605055), Postgraduate Research and Practice Innovation Project for Graduate Students of JiangSu Province, China (Grant No. KYCX18-2100), and the Scientific Research Funds of Huaqiao University, China (Grant No. 605-50Y17064).
Corresponding Authors:  Can Xu, Huaping Lü     E-mail:;

Cite this article: 

Tianwen Pan(潘天文), Xia Huang(黄霞), Can Xu(徐灿), Huaping Lü(吕华平) Relaxation dynamics of Kuramoto model with heterogeneous coupling 2019 Chin. Phys. B 28 120503

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