Stability and stabilization of Boolean networks with impulsive effects

Abstract This paper investigates the stability and stabilization of Boolean networks with impulsive effects. After giving a survey on semi-tensor product of matrices, we convert a Boolean network with impulsive effects into impulsive discrete-time dynamics. Then, some necessary and sufficient conditions are given for the stability and stabilization of Boolean networks with impulsive effects. Finally, examples are provided to illustrate the efficiency of the obtained results.

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

[2]  Arjan van der Schaft,et al.  A passivity-based approach to reset control systems stability , 2010, Syst. Control. Lett..

[3]  Daniel W. C. Ho,et al.  Stability, robust stabilization and H∞ control of singular-impulsive systems via switching control , 2006, Syst. Control. Lett..

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

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

[6]  Albert,et al.  Dynamics of complex systems: scaling laws for the period of boolean networks , 2000, Physical review letters.

[7]  John Maloney,et al.  Scalar equations for synchronous Boolean networks with biological applications , 2004, IEEE Transactions on Neural Networks.

[8]  Daizhan Cheng,et al.  Controllability and observability of Boolean control networks , 2009, Autom..

[9]  B. Goodwin.  Temporal organization in cells , 1963 .

[10]  Seddik M. Djouadi,et al.  On robust stabilization over communication channels in the presence of unstructured uncertainty , 2006, 2006 American Control Conference.

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

[12]  B. Drossel,et al.  Number and length of attractors in a critical Kauffman model with connectivity one. , 2004, Physical review letters.

[13]  M. Aldana.  Boolean dynamics of networks with scale-free topology , 2003 .

[14]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

[15]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

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

[17]  B. Samuelsson,et al.  Superpolynomial growth in the number of attractors in Kauffman networks. , 2003, Physical review letters.

[18]  Yiguang Hong,et al.  Finite-time stabilization and stabilizability of a class of controllable systems , 2002, Syst. Control. Lett..

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

[20]  Fangfei Li,et al.  Controllability of Boolean control networks with time delays in states , 2011, Autom..

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

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

[23]  Yu Zhang,et al.  Impulsive Control of Discrete Systems With Time Delay , 2009, IEEE Transactions on Automatic Control.

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