Synchronization in output-coupled temporal Boolean networks

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

doi:10.1038/srep06292

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 language	English
Article number	06292
Journal	Scientific Reports
Volume	4
DOIs	https://doi.org/10.1038/srep06292
Publication status	Published - 2014

Bibliographical note

The authors acknowledge the National Natural Science Foundation of China under Grant 61175119, Grant 61272530 and Grant 61203235, and IRTG 1740 (DFG and FAPESP). This publication was made possible by NPRP grant #NPRP 4-1162-1-181 from the Qatar

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10.1038/srep06292

Synchronization in output-coupled
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title = "Synchronization in output-coupled temporal Boolean networks",

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 ofan 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. ",

author = "Jianquan Lu and Jie Zhong and Yang Tang and Tingwen Huang and Jinde Cao and Jurgen Kurths",

note = "The authors acknowledge the National Natural Science Foundation of China under Grant 61175119, Grant 61272530 and Grant 61203235, and IRTG 1740 (DFG and FAPESP). This publication was made possible by NPRP grant #NPRP 4-1162-1-181 from the Qatar",

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AU - Lu, Jianquan

AU - Zhong, Jie

AU - Tang, Yang

AU - Huang, Tingwen

AU - Cao, Jinde

AU - Kurths, Jurgen

N1 - The authors acknowledge the National Natural Science Foundation of China under Grant 61175119, Grant 61272530 and Grant 61203235, and IRTG 1740 (DFG and FAPESP). This publication was made possible by NPRP grant #NPRP 4-1162-1-181 from the Qatar

PY - 2014

Y1 - 2014

N2 - 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 ofan 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.

AB - 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 ofan 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.

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SN - 2045-2322

VL - 4

JO - Scientific Reports

JF - Scientific Reports

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Synchronization in output-coupled temporal Boolean networks

Abstract

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