Partial Synchronization of Interconnected Boolean Networks

This paper addresses the partial synchronization problem for the interconnected Boolean networks (BNs) via the semi-tensor product (STP) of matrices. First, based on an algebraic state space representation of BNs, a necessary and sufficient criterion is presented to ensure the partial synchronizatio...

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Bibliographic Details
Published inIEEE transactions on cybernetics Vol. 47; no. 1; pp. 258 - 266
Main Authors Chen, Hongwei, Liang, Jinling, Lu, Jianquan
Format Journal Article
LanguageEnglish
Published United States IEEE 01.01.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Adjacency matrix
Biological system modeling
Boolean algebra
Boolean functions
Boolean networks (BNs)
Criteria
Cybernetics
Graph theory
Indexes
Integrated circuit interconnections
Oscillators
partial synchronization
semi-tensor product (STP)
State space models
Synchronism
Synchronization
Tensors
Yttrium
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Summary:This paper addresses the partial synchronization problem for the interconnected Boolean networks (BNs) via the semi-tensor product (STP) of matrices. First, based on an algebraic state space representation of BNs, a necessary and sufficient criterion is presented to ensure the partial synchronization of the interconnected BNs. Second, by defining an induced digraph of the partial synchronized states set, an equivalent graphical description for the partial synchronization of the interconnected BNs is established. Consequently, the second partial synchronization criterion is derived in terms of adjacency matrix of the induced digraph. Finally, two examples (including an epigenetic model) are provided to illustrate the efficiency of the obtained results.
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content type line 23
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2015.2513068