Partial Synchronization for Boolean Network Based on Pinning Control Strategy

In this paper, pinning controller designing for partial synchronization is studied for Boolean Networks in the drive-response structure. The problem can be converted into making the response BN stabilized into certain cycles under the certain switching signals. All limit cycles are found out, which can achieve partial synchronization. Partial synchronization is achieved by changing the transition matrix of the response BN. An algorithm for choosing pinning nodes and pinning controller design is obtained. Finally, a numerical example is given to show the efficiency of the design procedure.

[1]  Fuad E. Alsaadi,et al.  Set stabilization of Boolean networks under pinning control strategy , 2017, Neurocomputing.

[2]  Yiguang Hong,et al.  Solvability and control design for synchronization of Boolean networks , 2013, Journal of Systems Science and Complexity.

[3]  Daizhan Cheng,et al.  From STP to game-based control , 2017, Science China Information Sciences.

[4]  Shouwei Zhao,et al.  A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization. , 2011, Chaos.

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

[6]  Hongwei Chen,et al.  Partial Synchronization of Interconnected Boolean Networks , 2017, IEEE Transactions on Cybernetics.

[7]  M. Margaliot.  Controllability and observability of Boolean control networks , 2012 .

[8]  Kunihiko Kaneko,et al.  Relevance of dynamic clustering to biological networks , 1993, chao-dyn/9311008.

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

[10]  Yang Liu,et al.  Feedback Controller Design for the Synchronization of Boolean Control Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Daizhan Cheng,et al.  A Linear Representation of Dynamics of Boolean Networks , 2010, IEEE Transactions on Automatic Control.

[12]  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.

[13]  Tianguang Chu,et al.  Synchronization of Boolean networks with time delays , 2012, Appl. Math. Comput..

[14]  Nikolai F. Rulkov,et al.  Images of synchronized chaos: Experiments with circuits. , 1996, Chaos.

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

[16]  Peng Shi,et al.  Exponential Synchronization of Neural Networks With Discrete and Distributed Delays Under Time-Varying Sampling , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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

[18]  Dongdai Lin,et al.  Stability of nonlinear feedback shift registers , 2014, ICIA.

[19]  Fangfei Li,et al.  Pinning Control Design for the Stabilization of Boolean Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

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