On cycles of periodically time-variant Boolean networks

This paper investigates cycles of periodically time-variant Boolean networks (PTVBN). Firstly, compared with the time-invariant Boolean networks, new properties of cycles of PTVBN are revealed for the first time. Then, necessary and sufficient conditions for judging cycles of PTVBNs are obtained and consequently the method to search cycles is given. Finally, some examples are given to illustrate the obtained results.

[1]  Tao Li,et al.  A negative selection algorithm based on hierarchical clustering of self set , 2011, Science China Information Sciences.

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

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

[4]  Edward R. Dougherty,et al.  From Boolean to probabilistic Boolean networks as models of genetic regulatory networks , 2002, Proc. IEEE.

[5]  Michael Margaliot,et al.  Minimum-Time Control of Boolean Networks , 2013, SIAM J. Control. Optim..

[6]  S. Huang,et al.  Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. , 2000, Experimental cell research.

[7]  B. Luque,et al.  Random Boolean networks response to external periodic signals , 2002 .

[8]  Sui Huang.  Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery , 1999, Journal of Molecular Medicine.

[9]  Carsten Peterson,et al.  Random Boolean network models and the yeast transcriptional network , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[10]  D. Cheng,et al.  Semi-tensor Product of Matrices , 2011 .

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

[12]  Satoru Miyano,et al.  Identification of Genetic Networks from a Small Number of Gene Expression Patterns Under the Boolean Network Model , 1998, Pacific Symposium on Biocomputing.

[13]  Daizhan Cheng,et al.  Input-State Approach to Boolean Networks , 2009, IEEE Transactions on Neural Networks.

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

[15]  V. Cambiazo,et al.  Regulatory network for cell shape changes during Drosophila ventral furrow formation. , 2006, Journal of theoretical biology.

[16]  L. O’Driscoll.  Gene Expression Profiling , 2011, Methods in Molecular Biology.

[17]  Daizhan Cheng,et al.  Realization of Boolean control networks , 2010, Autom..

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

[19]  Edward R. Dougherty,et al.  The impact of function perturbations in Boolean networks , 2007, Bioinform..

[20]  Lijun Zhang,et al.  Controllability of time-variant Boolean control networks and its application to Boolean control networks with finite memories , 2012, Science China Information Sciences.

[21]  Yuzhen Wang,et al.  On reachability and controllability of switched Boolean control networks , 2012, Autom..

[22]  Daizhan Cheng,et al.  Optimal Control of Logical Control Networks , 2011, IEEE Transactions on Automatic Control.

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

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

[25]  Fangfei Li,et al.  Controllability and optimal control of a temporal Boolean network , 2012, Neural Networks.

[26]  Fangfei Li,et al.  Complete synchronization of temporal Boolean networks , 2013, Neural Networks.

[27]  Daizhan Cheng,et al.  Disturbance Decoupling of Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.