Intra-layer synchronization in duplex networks

doi:10.1088/1674-1056/27/10/100503

Abstract

This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly, for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results.

Keywords: multi-layer network intra-layer synchronization Lyapunov stability method

Received: 08 June 2018
Revised: 17 July 2018
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund:

Project supported in part by the National Natural Science Foundation of China (Grant Nos. 61573004 and 11501221), the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQN-YX301), the Program for New Century Excellent Talents in Fujian Province University in 2016, and the Project of Education and Scientific Research for Middle and Young Teachers in Fujian Province, China (Grant Nos. JAT170027 and JA15030).

Corresponding Authors: Longkun Tang
E-mail: tomlk@hqu.edu.cn

Cite this article:

Jie Shen(沈洁), Longkun Tang(汤龙坤) Intra-layer synchronization in duplex networks 2018 Chin. Phys. B 27 100503

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