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Cognitive Neurodynamics

Erschienen in:

01.09.2010 | Original Research

Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic

verfasst von: Qi Luo, Rubei Zhang, Xiaoxin Liao

Erschienen in: Cognitive Neurodynamics | Ausgabe 3/2010

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Abstract

In this paper, the global exponential stability in Lagrange sense for genetic regulatory networks (GRNs) with SUM regulatory logic is firstly studied. By constructing appropriate Lyapunov-like functions, several criteria are presented for the boundedness, ultimate boundedness and global exponential attractivity of GRNs. It can be obtained that GRNs with SUM regulatory logic are unconditionally globally exponentially stable in Lagrange sense. These results can be applied to analyze monostable as well as multistable networks. Furthermore, to analyze the stability for GRNs more comprehensively, the existence of equilibrium point of GRNs is proved, and some sufficient conditions of the global exponential stability in Lyapunov sense for GRNs are derived. Finally two numerical examples are given to illustrate the application of the obtained results.

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Becskei A, Serrano L (2000) Engineering stability in gene networks by autoregulation. Nature 405:590–593CrossRefPubMed

Bolouri H, Davidson EH (2002) Modeling transcriptional regulatory networks. Bio Essays 24:1118–1129

Chaouiya C, Remy E, Ruet P, Thieffry D (2008) Petri net modeling of biological regulatory networks. J Discrete Algorithms 6:165–177CrossRef

Chen L, Aihara K (2002) Stability of genetic regulatory networks with time delay. IEEE Trans Circuits Syst I Fundam Theory Appl 49:602–608CrossRef

Chen YY, Luo Q (2009) Global exponential stability in Lagrange sense for a class of neural networks. J Nanjing Univ Inf Sci Technol Nat Sci Ed 1(1):50–58

Chen T, He H, Church GM (1999) Modeling gene expression with differential equations. Proc Pac Symp Biocomputing 4:29–40

Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403:335–338CrossRefPubMed

Friedman N, Linial M, Nachman I, Pe’er D (2000) Using Bayesian networks to analyze expression data. J Comput Biol 7:601–620CrossRefPubMed

Gardner T, Cantor C, Collins J (2000) Construction of a genetic toggle switch in Escherichia coli. Nature 403:339–342CrossRefPubMed

Goodwin BC (1963) Temporal organization in cells. Academic Press, New York

Hardy S, Robillard PN (2004) Modeling and simulation of molecular biology systems using Petri nets: modeling goals of various approaches. J Bioinform Comput Biol 2:595–613CrossRefPubMed

Hartemink AJ, Gifford DK, Jaakkola TS, Young RA (2002) Bayesian methods for elucidating genetic regulatory networks. IEEE Intell Syst 17:37–43

Hassibi A, Boyd SP, How JP (1999) A class of Lyapunov functionals for analyzing hybrid dynamical systems. In: Proceedings of American Control Conference, San Diego, California, June, 1999

Jong HD (2002) Modelling and simulation of genetic regulatory systems: a literature review. J Comput Biol 9:67–103CrossRefPubMed

Kalir S, Mangan S, Alon U (2005) A coherent feed-forward loop with a SUM input function prolongs flagella expression in Escherichia coli. Mol Syst Biol. doi: 10.1038/msb4100010

LaSalle J (1960) Some extensions of Liapunov’s second method. IEEE Trans Circuit Theory 7(4):520–527

Li C, Chen L, Aihara K (2006a) Synchronization of coupled nonidentical genetic oscillators. Phys Biol 3:37–44CrossRefPubMed

Li C, Chen L, Aihara K (2006b) Stability of genetic networks with sum regulatory logic: Lur’e system and LMI approach. IEEE Trans Circuits Syst I 53(11):2451–2458CrossRef

Liao XX (2000) Theory and application of stability for dynamical system. National Defense Industry Press, Beijing

Liao XX, Wang J (2003) Global dissipativity of continuous-time recurrent neural networks. Phys Rev E 68(016118):1–4

Liao XX, Luo Q, Zeng ZG, Guo YX (2008a) Global exponential stability in Lagrange sense for recurrent neural networks with time delays. Nonlinear Anal RWA 9:1535–1557CrossRef

Liao XX, Luo Q, Zeng ZG (2008b) Positive invariant and global exponential attractive sets of neural networks with time-varying delays. Neurocomputing 71:513–518CrossRef

Passino KM, Burgess KL (1995) Lagrange stability and boundedness of discrete event systems. Discrete Event Dyn Syst Theory Appl 5:383–403CrossRef

Pease A, Solas D, Sullivan E, Cronin M, Holmes C, Fodor S (1994) Light-generated oligonucleotide arrays for rapid DNA sequence analysis. Proc Natl Acad Sci USA 91(11):5022–5026CrossRefPubMed

Rekasius ZV (1963) Lagrange stability of nonlinear feedback systems. IEEE Trans Automat Control 8(2):160–163CrossRef

Ren F, Cao J (2008) Asymptotic and robust stability of genetic regulatory networks with time-varying delays. Neurocomputing 71:834–842CrossRef

Smolen P, Baxter DA, Byrne JH (2000) Mathematical modeling of gene networks review. Neuron 26:567–580CrossRefPubMed

Somogyi R, Sniegoski C (1996) Modeling the complexity of genetic networks: understanding multigenic and pleiotropic regulation. Complexity 1:45–63

Thornton KW, Mulholland RJ (1974) Lagrange stability and ecological systems. J Theor Biol 45:473–485CrossRefPubMed

Tian T, Burragea K, Burragea PM, Carlettib M (2007) Stochastic delay differential equations for genetic regulatory networks. J Comput Appl 205:696–707CrossRef

Wang GJ, Cao JD (2009) Robust exponential stability analysis for stochastic genetic networks with uncertain parameters. Commun Nonlinear Sci Numer Simul 14:3369–3378CrossRef

Wang R, Zhang Z (2007) Energy coding in biological neural networks. Cogn Neurodyn 1(3):203–212CrossRefPubMed

Wang J, Duan Z, Huang L (2006) Control of a class of pendulum-like systems with Lagrange stability. Automatica 42:145–150CrossRef

Wang ZX, Liao XF et al (2009) Robust stability of stochastic genetic regulatory networks with discrete and distributed delays. Soft Comput 13:1199–1208CrossRef

Weaver DC, Workman CT, Storm GD (1999) Modeling regulatory networks with weight matrices. Proc Pac Symp Biocomput 4:113–123

Yang Y, Huang L (2006) Lagrange stability of a class of nonlinear discrete-time systems. In: First IEEE conference on industrial electronics and applications, May 2006, pp 1–6

Yi Z, Tan KK (2004) Convergence analysis of recurrent neural networks. Kluwer, Dordrecht

Yoshizawa T (1966) Stability theory by Liapunov’s second method. Mathematical Society of Japan, Tokyo

Yuh CH, Bolouri H, Davidson EH (1998) Genomic cis-regulatory logic: experimental and computational analysis of a sea urchin gene. Science 279:1896–1902CrossRefPubMed

Titel: Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic
verfasst von: Qi Luo
Rubei Zhang
Xiaoxin Liao
Publikationsdatum: 01.09.2010
Verlag: Springer Netherlands
Erschienen in: Cognitive Neurodynamics / Ausgabe 3/2010
Print ISSN: 1871-4080
Elektronische ISSN: 1871-4099
DOI: https://doi.org/10.1007/s11571-010-9113-1

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