Robust stability of stochastic delayed genetic regulatory networks

Cognitive Neurodynamics

Volumn 3, Issue 3, 2009, Pages 271-280

  Wang, Zhengxia ^a,b   Liu, Guodong ^a   Sun, Yanhong ^a   Wu, Hongli ^c  

^a CHONGQING JIAOTONG UNIVERSITY   (China)

^b CHONGQING UNIVERSITY   (China)

^c Hainan Normal College   (China)

Author keywords

Genetic network; Robust stability; Stochastic perturbation; Time varying delays; Uncertain system

Indexed keywords

ARTICLE; GENETIC REGULATION; NOISE; STATISTICAL ANALYSIS; STOCHASTIC MODEL;

EID: 69049086492     PISSN: 18714080     EISSN: 18714099     Source Type: Journal    
DOI: 10.1007/s11571-009-9077-1     Document Type: Article

References (29)

1. A Becskei L Serrano 2000 Engineering stability in gene networks by autoregulation Nature 405 590 593 10.1038/35014651
2. L Benuskova N Kasabov 2008 Modeling brain dynamics using computational neurogenetic approach Cogn Neurodyn 2 319 334 10.1007/s11571-008-9061-1
3. H Bolouri EH Davidson 2002 Modelling transcriptional regulatory networks BioEssay 24 1118 1129 10.1002/bies.10189
4. Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia
5. JD Cao FL Ren 2008 Exponential stability of discrete-time genetic regulatory networks with delays IEEE Trans Neural Netw 19 3 520 523 10.1109/TNN.2007.911748
6. LN Chen K Aihara 2002 Stability of genetic regulatory networks with time delay IEEE Trans Circuits Syst I Fundam Theory Appl 49 5 602 608 10.1109/TCSI.2002.1001949
7. LN Chen RQ Wang et al 2004 Dynamics of gene regulatory networks with cell division cycle Phys Rev E Stat Nonlin Soft Matter Phys 70 011909 10.1103/PhysRevE.70.011909
8. H De Jong 2002 Modeling and simulation of genetic regulatory systems: a literature review J Comput Biol 9 67 103 10.1089/10665270252833208
9. MB Elowitz S Leibler 2000 A synthetic oscillatory network of transcriptional regulators Nature 403 335 338 10.1038/35002125
10. Gahinet P, Nemirovski A, Laub A, Chialali M (1995) LMI control toolbox user's guide. The Mathworks, Natick
11. Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference on decision and control. Sydney, Australia, pp 2805-2810
12. J Hasty J Pradines M Dolnik J Collins 2000 Noised-based switches and amplifiers for gene expressions Proc Natl Acad Sci USA 97 5 2075 2080 10.1073/pnas.040411297
13. J Hasty D McMillen F Isaacs JJ Collins 2001 Computational studies of gene regulatory networks: in numero molecular biology Nat Rev Genet 2 268 279 10.1038/35066056
14. WL He JD Cao 2008 Robust stability of genetic regulatory networks with distributed delay Cogn Neurodyn 2 355 361 10.1007/s11571-008-9062-0
15. H Huang G Feng 2007 Delay-dependent stability for uncertain stochastic neural networks with time-varying delay Physica A 381 93 103 10.1016/j.physa.2007.04.020
16. T Kobayashi L Chen K Aihara 2002 Modeling genetic switches with positive feedback loops J Theor Biol 221 379 399 10.1006/jtbi.2003.3190
17. CG Li LN Chen K Aihara 2006 Stability of genetic networks with SUM regulatory logic: Lur'e system and LMI approach IEEE Trans Circuits Syst I Regul Pap 53 11 2451 2458 10.1109/TCSI.2006.883882
18. CG Li LN Chen K Aihara 2006 Synchronization of coupled nonidentical genetic oscillators Phys Biol 3 37 44 10.1088/1478-3975/3/1/004
19. XF Liao K-W Wong Z Wu G Chen 2001 Novel robust stability criteria for interval-delayed Hopfield neural networks IEEE Trans Circuits Syst I 48 11 1355 1359 10.1109/81.964428
20. XF Liao GR Chen ZEN Sanche 2002 LMI-based approach for asymptotical stability analysis of delayed neural network IEEE Tans Circuits Syst I 49 7 1033 1039 10.1109/TCSI.2002.800842
21. Oksendal B (2003) Stochastic differential equations, 4th edn. Springer-Verlag, New York
22. FL Ren JD Cao 2008 Asymptotic and robust stability of genetic regulatory networks with time-varying delays Neurocomputing 71 834 842 10.1016/j.neucom. 2007.03.011
23. P Smolen DA Baxter JH Byrne 2000 Mathematical modeling of gene networks Neuron 26 567 580 10.1016/S0896-6273(00)81194-0
24. TE Turner S Schnell K Burrage 2004 Stochastic approaches for modelling in vivo reactions Comput Biol Chem 28 165 178 10.1016/j.compbiolchem.2004.05.001
25. R Wang T Zhou Z Jing L Chen 2004 Modelling periodic oscillation of biological systems with multiple time scale networks Syst Biol 1 71 84 10.1049/sb:20045007
26. ZD Wang H Shu J Fang X Liu 2006 Robust stability for stochastic Hopfield neural networks with time delays Nonlinear Anal Real World Appl 7 5 1119 1128 10.1016/j.nonrwa.2005.10.004
27. ZD Wang S Lauria J Fang X Liu 2007 Exponential stability of uncertain stochastic neural networks with mixed time-delays Chaos, Solitons Fractals 32 62 72 10.1016/j.chaos.2005.10.061
28. CH Yuh H Bolouri EH Davidson 1998 Genomic cis-regulatory logic: experimental and computational analysis of a sea urchin gene Science 279 1896 1902 10.1126/science.279.5358.1896
29. JH Zhang P Shi JQ Qiu 2007 Novel roubust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays Nonlinear Anal Real World Appl 8 1349 1357 10.1016/j.nonrwa.2006.06.010