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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
Issue 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.
ISSN: 0025-5564
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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