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 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.

[1]  Ju H. Park,et al.  Finite-time synchronization control for uncertain Markov jump neural networks with input constraints , 2014, Nonlinear Dynamics.

[2]  H. Cerdeira,et al.  Partial synchronization and spontaneous spatial ordering in coupled chaotic systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Michael Margaliot,et al.  A Maximum Principle for Single-Input Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

[4]  Meng Min,et al.  Synchronization of interconnected multi-valued logical networks , 2013, Proceedings of the 32nd Chinese Control Conference.

[5]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[6]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[7]  Jinde Cao,et al.  On Pinning Controllability of Boolean Control Networks , 2016, IEEE Transactions on Automatic Control.

[8]  B. Goodwin.  Temporal Organization in Cells; a Dynamic Theory of Cellular Control Processes , 2015 .

[9]  Mohammad Bagher Menhaj,et al.  Fuzzy Complex Dynamical Networks and Its Synchronization , 2013, IEEE Transactions on Cybernetics.

[10]  T. Chu,et al.  Synchronization in an array of coupled Boolean networks , 2012 .

[11]  Daizhan Cheng,et al.  On controllability and stabilizability of probabilistic Boolean control networks , 2012, Science China Information Sciences.

[12]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

[13]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[14]  Jesus M. Gonzalez-miranda,et al.  Synchronization And Control Of Chaos: An Introduction For Scientists And Engineers , 2004 .

[15]  Panos Louvieris,et al.  Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Yang Liu,et al.  Synchronisation analysis of Boolean networks based on equivalence , 2015 .

[17]  Yuzhen Wang,et al.  Consistent stabilizability of switched Boolean networks , 2013, Neural Networks.

[18]  Michael Margaliot,et al.  Controllability of Boolean control networks via the Perron-Frobenius theory , 2012, Autom..

[19]  Jinde Cao,et al.  Synchronization in an Array of Output-Coupled Boolean Networks With Time Delay , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Fangfei Li.  Synchronization of coupled large-scale Boolean networks. , 2014, Chaos.

[21]  Huai-Ning Wu,et al.  Synchronization and Adaptive Control of an Array of Linearly Coupled Reaction-Diffusion Neural Networks With Hybrid Coupling , 2014, IEEE Transactions on Cybernetics.

[22]  Dimos V. Dimarogonas,et al.  Event-triggered control for discrete-time systems , 2010, Proceedings of the 2010 American Control Conference.

[23]  D. Cheng,et al.  Stability and stabilization of Boolean networks , 2011 .

[24]  F. Jiménez-Morales,et al.  Cellular automaton model for the simulation of laser dynamics. , 2003 .

[25]  Jiandong Zhu,et al.  System decomposition with respect to inputs for Boolean control networks , 2014, Autom..

[26]  J. Kurths,et al.  Structure–function relationship in complex brain networks expressed by hierarchical synchronization , 2007 .

[27]  M. Ng,et al.  Control of Boolean networks: hardness results and algorithms for tree structured networks. , 2007, Journal of theoretical biology.

[28]  Tianguang Chu,et al.  Complete Synchronization of Boolean Networks , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Hao Shen,et al.  Extended dissipativity-based synchronization of uncertain chaotic neural networks with actuator failures , 2015, J. Frankl. Inst..

[30]  John Maloney,et al.  Finding Cycles in Synchronous Boolean Networks with Applications to Biochemical Systems , 2003, Int. J. Bifurc. Chaos.

[31]  Chu Tianguang,et al.  General synchronization of multi-valued logical networks , 2012, Proceedings of the 31st Chinese Control Conference.

[32]  Daizhan Cheng,et al.  Analysis and Control of Boolean Networks , 2011 .

[33]  Jinde Cao,et al.  Synchronization Analysis of Master-Slave Probabilistic Boolean Networks , 2015, Scientific Reports.

[34]  Daizhan Cheng,et al.  Input-state incidence matrix of Boolean control networks and its applications , 2010, Syst. Control. Lett..

[35]  Hao Shen,et al.  Non-fragile mixed ℋ∞/l 2 − l ∞ synchronisation control for complex networks with Markov jumping-switching topology under unreliable communication links , 2014 .

[36]  Daizhan Cheng,et al.  On finite potential games , 2014, Autom..

[37]  Ettore Fornasini,et al.  Optimal Control of Boolean Control Networks , 2014, IEEE Transactions on Automatic Control.

[38]  Tingwen Huang,et al.  Passivity and Synchronization of Linearly Coupled Reaction-Diffusion Neural Networks With Adaptive Coupling , 2015, IEEE Transactions on Cybernetics.

[39]  Hao Zhang,et al.  Synchronization of Boolean Networks with Different Update Schemes , 2014, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[40]  Qi Li,et al.  Event-triggered synchronization control for complex networks with uncertain inner coupling , 2015, Int. J. Gen. Syst..