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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/4698

Title: On multistability of delayed genetic regulatory networks with multivariable regulation functions
Authors: Pan, W
Wang, Z
Gao, H
Li, Y
Du, M
Keywords: Multistability
Multivariable regulation function
Genetic regulatory networks
Lyapunov–Krasovskii functional
Linear matrix inequality
Multiple time delays
Publication Date: 2010
Publisher: Elsevier
Citation: Mathematical Biosciences 228(1): 100-109, Nov 2010
Abstract: Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov–Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results.
Description: The official published version of the article can be found at the link below.
Sponsorship: This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Royal Society of the UK, the National Natural Science Foundation of China under Grant 61028008, and the International Science and Technology Cooperation Project of China under Grant 2009DFA32050.
URI: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VHX-50XV9K0-2&_user=545641&_coverDate=11%2F30%2F2010&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1623107752&_rerunOrigin=google&_acct=C000027918&_version=1&_urlVersion=0&_userid=545641&md5=90897d7a7c8488029288842bd0183071&searchtype=a
http://bura.brunel.ac.uk/handle/2438/4698
DOI: http://dx.doi.org/10.1016/j.mbs.2010.08.012
ISSN: 0025-5564
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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