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Adaptive control of dynamical synchronization on evolving networks with noise disturbances

Wu-Jie Yuan1,2,*, Jian-Fang Zhou1, Irene Sendiña-Nadal3,4, Stefano Boccaletti5, and Zhen Wang6,†

  • 1College of Physics and Electronic Information, Huaibei Normal University, Huaibei 235000, China
  • 2College of Information, Huaibei Normal University, Huaibei 235000, China
  • 3Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
  • 4Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
  • 5CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy
  • 6School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, China

  • *yuanwj2005@163.com
  • †zhenwang0@gmail.com
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Phys. Rev. E 97, 022211 – Published 9 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022211

Abstract

In real-world networked systems, the underlying structure is often affected by external and internal unforeseen factors, making its evolution typically inaccessible. An adaptive strategy was introduced for maintaining synchronization on unpredictably evolving networks [Sorrentino and Ott, Phys. Rev. Lett. 100, 114101 (2008)], which yet does not consider the noise disturbances widely existing in networks' environments. We provide here strategies to control dynamical synchronization on slowly and unpredictably evolving networks subjected to noise disturbances which are observed at the node and at the communication channel level. With our strategy, the nodes' coupling strength is adaptively adjusted with the aim of controlling synchronization, and according only to their received signal and noise disturbances. We first provide a theoretical analysis of the control scheme by introducing an error potential function to seek for the minimization of the synchronization error. Then, we show numerical experiments which verify our theoretical results. In particular, it is found that our adaptive strategy is effective even for the case in which the dynamics of the uncontrolled network would be explosive (i.e., the states of all the nodes would diverge to infinity).

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Phys. Rev. E 97, 022211– Published 9 February, 2018
  • Received 22 August 2017
  • Revised 27 January 2018
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