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Disturbance Analysis of Nonlinear Differential Equation Models of Genetic SUM Regulatory Networks
January-February 2011 (vol. 8 no. 1)
pp. 253-259
Ping Li, The University of Hong Kong, Hong Kong
James Lam, The University of Hong Kong, Hong Kong
Noise disturbances and time delays are frequently met in cellular genetic regulatory systems. This paper is concerned with the disturbance analysis of a class of genetic regulatory networks described by nonlinear differential equation models. The mechanisms of genetic regulatory networks to amplify (attenuate) external disturbance are explored, and a simple measure of the amplification (attenuation) level is developed from a nonlinear robust control point of view. It should be noted that the conditions used to measure the disturbance level are delay-independent or delay-dependent, and are expressed within the framework of linear matrix inequalities, which can be characterized as convex optimization, and computed by the interior-point algorithm easily. Finally, by the proposed method, a numerical example is provided to illustrate how to measure the attenuation of proteins in the presence of external disturbances.

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Index Terms:
Disturbance attenuation, asymptotic stability, genetic regulatory network, systems biology, time delay.
Ping Li, James Lam, "Disturbance Analysis of Nonlinear Differential Equation Models of Genetic SUM Regulatory Networks," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 1, pp. 253-259, Jan.-Feb. 2011, doi:10.1109/TCBB.2010.19
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