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 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.
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China.
authors.forename: Jianquan
authors.initials: J
authors.lastname: Lu
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China.
authors.forename: Jie
authors.initials: J
authors.lastname: Zhong
authors.affiliation: 1] Potsdam Institute for Climate Impact Research, Potsdam 14415, Germany [2] Institute of Physics, Humboldt University of Berlin, Berlin 12489, Germany.
authors.forename: Yang
authors.initials: Y
authors.lastname: Tang
authors.affiliation: Texas A&M University at Qatar, Doha 23874, Qatar.
authors.forename: Tingwen
authors.initials: T
authors.lastname: Huang
authors.affiliation: 1] Department of Mathematics, Southeast University, Nanjing 210096, China [2] Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
authors.affiliation: 1] Potsdam Institute for Climate Impact Research, Potsdam 14415, Germany [2] Institute of Physics, Humboldt University of Berlin, Berlin 12489, Germany [3] Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths