Controlling synchronous patterns in complex networks

Weijie Lin, Huawei Fan, Ying Wang, Heping Ying, and Xingang Wang
Phys. Rev. E 93, 042209 – Published 18 April 2016

Abstract

Although the set of permutation symmetries of a complex network could be very large, few of them give rise to stable synchronous patterns. Here we present a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators. Specifically, according to the network permutation symmetry, we design a small-size and weighted network, namely the control network, and use it to control the large-size complex network by means of pinning coupling. We argue mathematically that for any of the network symmetries, there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized. The feasibility of the control method is verified by numerical simulations of both artificial and real-world networks and demonstrated experimentally in systems of coupled chaotic circuits. Our studies show the controllability of synchronous patterns in complex networks of coupled chaotic oscillators.

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  • Received 9 November 2015
  • Revised 30 March 2016

DOI:https://doi.org/10.1103/PhysRevE.93.042209

©2016 American Physical Society

Physics Subject Headings (PhySH)

NetworksNonlinear Dynamics

Authors & Affiliations

Weijie Lin1,2, Huawei Fan2, Ying Wang2, Heping Ying1, and Xingang Wang2,3,*

  • 1Department of Physics, Zhejiang University, Hangzhou 310027, China
  • 2School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
  • 3Institute of Theoretical & Computational Physics, Shaanxi Normal University, Xi'an 710062, China

  • *wangxg@snnu.edu.cn

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Vol. 93, Iss. 4 — April 2016

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