Solvability and control design for synchronization of Boolean networks

Journal of Systems Science and Complexity

Volumn 26, Issue 6, 2013, Pages 871-885

  Xu, Xiangru ^a   Hong, Yiguang ^a  

^a CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Boolean networks; open loop and feedback control; semi tensor product; synchronization

Indexed keywords

COMPUTER CIRCUITS; FEEDBACK CONTROL; MATRIX ALGEBRA; SYNCHRONIZATION;

BOOLEAN NETWORKS; CONSTRUCTIVE DESIGN; MATRIX EXPRESSION; OPEN LOOP CONTROL; OPEN-LOOP; SEMI-TENSOR PRODUCT; SOLVABILITY CONDITIONS; SYNCHRONIZATION PROBLEM;

DESIGN;

EID: 84890423751     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-013-2040-6     Document Type: Article

References (26)

1. Kauffman S, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theoretical Biology, 1969, 22: 437-467.
2. Kunz W and Stoffel D, Reasoning in Boolean Networks: Logic Synthesis and Verification Using Testing Techniques, Kluwer Academic Publishers, Boston, 1997.
3. Kauffman S, The Origins of Order: Self-organization and Selection in Evolution, Oxford University Press, New York, 1993.
4. Farrow C, Heidel J, Maloney J, and Roger J, Scale equations for synchronous Boolean networks with biological applications, IEEE Trans. Neural Networks, 2004, 15(2): 348-354.
5. Cheng D, Qi H, Li Z Q, Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach, Springer, London, 2010.
6. Ma J, Cheng D, Hong Y, and Sun Y, On complexity of power systems, Journal of Systems Science and Complexity, 2003, 16(3): 391-403.
7. Zhao Y, Li Z, and Cheng D, Optimal control of logical control networks, IEEE Trans. Automatical Control, 2011, 56(8): 1766-1776.
8. Cheng D and Qi H, Controllability and observability of Boolean control networks, Automatica, 2009, 45(7): 1659-1667.
9. Cheng D, Qi H, Hu X, and Liu J, Stability and stabilization of Boolean networks, Int. J. Rubost and Nonlinear Control, 2010, 21(2): 134-156.
10. Laschov D and Margaliot M, A maximum principle for single-input of Boolean control network, IEEE Trans. Automatic Control, 2011, 56(4): 913-917.
11. Li F and Sun J, Controllability of Boolean control networks with time delays in states, Automatica, 2011, 47(3): 603-607.
12. Danino T, Mondragon-Palomino O, Tsimiring L, et al., A synchronized quorum of genetic clocks, Nature, 2010, 463: 326-330.
13. Hong Y, Qin H, and Chen G, Adaptive synchronization of chaotic systems via state and output feedback, Int. J. of Bifurcation and Chaos, 2001, 11(5): 1149-1158.
14. Morelli L G and Zanette D H, Synchronization of Kauffman networks, Phys. Rev. E, 2001, 63(3): 036204-1-036204-10.
15. Millérioux G and Guillot P, Self-synchronizing stream ciphers and dynamical systems: State of the art and open issues, Int. Journal of Bifurcation and Chaos, 2010, 20(9): 2979-2991.
16. Glass L, Synchronization and rhythmic processes in physiology, Nature, 2001, 410: 277-284.
17. Ballesteros F and Luque B, Random Boolean networks response to external periodic signals, Physica A, 2002, 313: 289-300.
18. Hung Y C, Ho M C, Lih J S, and Jiang I M, Chaos synchronization of two stochastically coupled random Boolean networks, Phys. Lett. A, 2006, 356(1): 35-43.
19. Hong Y and Xu X, Solvability and control design for dynamic synchronization of Boolean networks, 29th Chinese Control Conference, Beijing, China, 2010, 805-810.
20. Akutsu T, Hayashida M, Ching W, and Ng M K, Control of Boolean networks: Hardness results and algorithms for tree structured networks, J. Theoretical Biology, 2007, 244: 670-679.
21. Ho M C, Hung Y C, and Jiang I M, Stochastic coupling of two random Boolean networks, Phys. Lett. A, 2005, 344(1): 36-42.
22. Robert F, Discrete Iterations: A Metric Study, Translated by Rokne J, Springer-Verlag, Berlin, 1986.
23. Tutte W T, Graph Theory, Cambridge University Press, UK, 2001.
24. Huepe-Minoletti C and Aldana-Gonzalez M, Dynamical phase transition in a neural network model with noise: An exact solution, Journal of Statistical Physics, 2002, 108: 527-540.
25. Kitano H, Cancer as a robust system: Implications for anticancer therapy, Nature Reviews Cancer, 2004, 4(3): 227-235.
26. Huang J, Nonlinear Output Regulation: Theory & Applications, SIAM, Phildelphia, 2004.