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Chin. Phys. B, 2011, Vol. 20(10): 108701    DOI: 10.1088/1674-1056/20/10/108701
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY Prev   Next  

Stability of piecewise-linear models of genetic regulatory networks

Lin Peng(林鹏), Qin Kai-Yu(秦开宇), and Wu Hai-Yan(吴海燕)
Institute of Astronautics and Aeronautics, University of Electronic Science and Technology of China, Chengdu 610054, China
Abstract  This paper investigates the stability of the equilibria of the piecewise-linear models of genetic regulatory networks on the intersection of the thresholds of all variables. It first studies circling trajectories and derives some stability conditions by quantitative analysis in the state transition graph. Then it proposes a common Lyapunov function for convergence analysis of the piecewise-linear models and gives a simple sign condition. All the obtained conditions are only related to the constant terms on the right-hand side of the differential equation after bringing the equilibrium to zero.
Keywords:  genetic regulatory networks      piecewise-linear model      Lyapunov function  
Received:  29 November 2010      Revised:  13 April 2011      Accepted manuscript online: 
PACS:  87.18.Vf (Systems biology)  
  87.85.Xd (Dynamical, regulatory, and integrative biology)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60672029).

Cite this article: 

Lin Peng(林鹏), Qin Kai-Yu(秦开宇), and Wu Hai-Yan(吴海燕) Stability of piecewise-linear models of genetic regulatory networks 2011 Chin. Phys. B 20 108701

[1] Alur R, Belta C, Ivanicic F, Kumar V, Mintz F, Pappas G, Rubin H and Schug J 2001 Lecture Notes in Computer Science 2034 19
[2] Angeli D and Sontag E 2008 IEEE Trans. Autom. Control 53 166
[3] Azuma S, Yanagisawa E and Imura J 2008 IEEE Trans. Autom. Control 53 139
[4] Batt G, Ropers D, de Jong H, Geiselmann J, Mateescu R, Page M and Schneider D 2005 Bioinformatics 21 i19
[5] Casey R, de Jong H and Gouz'e J 2006 J. Math. Biol. 52 27
[6] Chaves M, Eissing T and Allöwger F 2008 IEEE Trans. Autom. Control 53 87
[7] de Jong H 2002 J. Comput. Biol. 9 67
[8] de Jong H, Gouz'e J, Hernandez C E, Page M and Sari T 2004 Bull. Math. Biol. 66 301
[9] Drulhe S, Ferrari-Trecate G, de Jong H and Viari A 2006 Hybrid Systems: Computation and Control 3927 184
[10] Edwards R 2000 Physica D 146 165
[11] Farcot E and Gouze J 2009 Acta Biotheor. 57 429
[12] Farcot E 2006 J. Math. Biol. 52 373
[13] Glass L and Kauffman S 1972 J. Theor. Biol. 34 219
[14] Glass L and Kauffman S 1973 J. Theor. Biol. 39 103
[15] Glass L and P'erez R 1974 J. Chem. Phys. 61 5242
[16] Ghosh R, Tiwari A and Tomlin C 2003 Hybrid Systems: Computation and Control 1790 233
[17] Goodwin B 1965 Advances in Enzyme Regulation 3 425
[18] Gouz'e J and Sari T 2002 Dyn. Syst. 17 299
[19] Mestl T, Plahte E and Omholt S 1995 J. Theor. Biol. 176 291
[20] Plahte E, Mestl T and Omholt S 1998 J. Math. Biol. 36 36
[21] Snoussi E and Thomas R 1993 Bull. Math. Biol. 55 973
[22] Snoussi E 1989 Dyn. Stab. Syst. 4 189
[23] Gao L, Shi J and Guan S 2010 Chin. Phys. B 19 010512
[24] Gao J, Jiang L and Xu Z 2009 Chin. Phys. B 18 4571
[25] Wang X, Shen Y and Zhang L 2009 Chin. Phys. B 18 1684
[26] Johansson M 2002 Picewise Linear Cortrol Systems: A Computational Approach (Berlin, New York: Springer)
[27] Liberzon D 2003 Theory of Functional Differential Equations (Boston: Birkh"auser)
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