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Delay-Independent Stability of Genetic Regulatory Networks

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1 Author(s)
Fang-Xiang Wu ; Dept. of Mech. Eng., Univ. of Saskatchewan, Saskatoon, SK, Canada

Genetic regulatory networks can be described by nonlinear differential equations with time delays. In this paper, we study both locally and globally delay-independent stability of genetic regulatory networks, taking messenger ribonucleic acid alternative splicing into consideration. Based on nonnegative matrix theory, we first develop necessary and sufficient conditions for locally delay-independent stability of genetic regulatory networks with multiple time delays. Compared to the previous results, these conditions are easy to verify. Then we develop sufficient conditions for global delay-independent stability for genetic regulatory networks. Compared to the previous results, this sufficient condition is less conservative. To illustrate theorems developed in this paper, we analyze delay-independent stability of two genetic regulatory networks: a real-life repressilatory network with three genes and three proteins, and a synthetic gene regulatory network with five genes and seven proteins. The simulation results show that the theorems developed in this paper can effectively determine the delay-independent stability of genetic regulatory networks.

Published in:

Neural Networks, IEEE Transactions on  (Volume:22 ,  Issue: 11 )

Date of Publication:

Nov. 2011

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