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Title: Monostability and multistability of genetic regulatory networks with different types of regulation functions
Authors: Pan, W
Wang, Z
Gao, H
Liu, X
Keywords: Monostability;Multistability;Genetic regulatory networks;Linear matrix inequality;Multiple time-varying delay
Issue Date: 2010
Publisher: Elsevier
Citation: Nonlinear Analysis: Real World Applications, 11(4): 3170-3185, Aug 2010
Abstract: Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by applying control theory and mathematical tools. The genetic regulatory networks (GRNs) with multiple time-varying delays and different types of regulation functions are considered. By putting forward a general sector-like regulation function and utilizing up-to-date techniques, a novel Lyapunov–Krasovskii functional is introduced for achieving delay dependence to ensure less conservatism. A new condition is then proposed for the general stability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the upper and lower bounds of the delays. Our general stability conditions are applicable to several frequently used regulation functions. It is shown that the existing results for monostability of GRNs are special cases of our main results. Five 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.
ISSN: 1468-1218
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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