Synchronisation analysis of Boolean networks based on equivalence

Hongwei Chen; Jinling Liang; Yang Liu; Tingwen Huang

Synchronisation analysis of Boolean networks based on equivalence

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Author(s): Hongwei Chen ¹ ; Jinling Liang ¹ ; Yang Liu ^{1, 2} ; Tingwen Huang ³
- Affiliations: 1: Department of Mathematics, Southeast University, Nanjing 210096, People's Republic of China ;
  2: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, People's Republic of China ;
  3: Science Program, Texas A&M University, Doha, Qatar
Source: Volume 9, Issue 15, 08 October 2015, p. 2242 – 2248
DOI: 10.1049/iet-cta.2015.0311 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 04/11/2014, Accepted 09/06/2015, Published 20/07/2015

This study studies the synchronisation of two Boolean networks (BNs) coupled in the drive-response configuration, and presents a number of new results. A new indicator variable, which plays an important role in characterising the synchronised nodes between the drive BN and the response BN, is defined by coordinate equivalence. Consequently, some necessary and sufficient conditions are derived for the general synchronisation of the drive-response BNs. Moreover, the upper bound of time to check the criterion is given. Two examples are provided to illustrate the efficiency of the obtained results.

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