Synchronization in output-coupled temporal Boolean networks

Jianquan Lu, Jie Zhong, Yang Tang, Tingwen Huang, Jinde Cao, Jurgen Kurths

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Abstract

This paper presents an analytical study of synchronization in an array of output-coupled temporal Boolean networks. A temporal Boolean network (TBN) is a logical dynamic system developed to model Boolean networks with regulatory delays. Both state delay and output delay are considered, and these two delays are assumed to be different. By referring to the algebraic representations of logical dynamics and using the semi-tensor product of matrices, the output-coupled TBNs are firstly converted into a discrete-time algebraic evolution system, and then the relationship between the states of coupled TBNs and the initial state sequence is obtained. Then, some necessary and sufficient conditions are derived for the synchronization of
an array of TBNs with an arbitrary given initial state sequence. Two numerical examples including one epigenetic model are finally given to illustrate the obtained results.
Original languageEnglish
Article number06292
JournalScientific Reports
Volume4
DOIs
Publication statusPublished - 2014

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    Lu, J., Zhong, J., Tang, Y., Huang, T., Cao, J., & Kurths, J. (2014). Synchronization in output-coupled temporal Boolean networks. Scientific Reports, 4, [06292]. https://doi.org/10.1038/srep06292