Enhancing network synchronizability by strengthening a single node

Huawei Fan, Yafeng Wang, Kai Yang, and Xingang Wang
Phys. Rev. E 99, 042305 – Published 16 April 2019

Abstract

In improving the stability of complex dynamical systems, an outstanding problem is how to achieve the desired performance at a low cost. For engineering and biological complex systems whose performance and functionality rely on the synchronous motion of their units, an important question related to the performance-cost-balance problem is how to improve efficiently the system synchronizability when a small amount of additional coupling resource is available. Here, employing a complex network of coupled chaotic oscillators as the model, we address this question by introducing a small amount of coupling intensity to only a single oscillator and investigate how the improvement of the network synchronizability is dependent on the location of the target oscillator. Theoretical analysis shows that, to achieve the maximum network synchronizability, the target oscillator to be strengthened should be chosen according to the eigenvector of the most unstable mode. Based on the theoretical finding, we further propose a single-node-based scheme for improving synchronization: the eigenvector-centrality-based strengthening scheme. We describe in detail how to apply this scheme under different synchronization scenarios and justify its efficiency in various network models by numerical simulations. The performance of the new scheme is compared with the conventional ones based on betweenness, closeness, and degree centralities, and it is shown that the new scheme has a clear advantage over the conventional ones. Furthermore, by a brute-force search of the target oscillator over the network, it is verified numerically that the oscillator identified by the new scheme indeed gives the best synchronization performance.

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  • Received 17 August 2018
  • Revised 2 December 2018

DOI:https://doi.org/10.1103/PhysRevE.99.042305

©2019 American Physical Society

Physics Subject Headings (PhySH)

NetworksNonlinear Dynamics

Authors & Affiliations

Huawei Fan, Yafeng Wang, Kai Yang, and Xingang Wang*

  • School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China

  • *wangxg@snnu.edu.cn

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Issue

Vol. 99, Iss. 4 — April 2019

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