Journal
NEUROCOMPUTING
Volume 174, Issue -, Pages 1060-1069Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.neucom.2015.10.024
Keywords
Genetic regulatory networks (GRNs); Time-varying discrete delays; Unbounded distributed delays; Globally asymptotic stability; M-matrix-based approach
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Funding
- National Natural Science Foundation of China [11371006, 61174126, 61222301]
- National Natural Science Foundation of Heilongjiang Province [F201326, A201416]
- fund of Heilongjiang Province Innovation Team Support Plan [2012TD007]
- Fund of Heilongjiang Education Committee [12541603]
- Fundamental Research Funds for the Central Universities [HIT.BRETIV.201303]
- Heilongjiang University Innovation Fund for Graduates [YJSCX2015-033HIJU]
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The problem of globally asymptotic stability for nonnegative equilibrium points of genetic regulatory networks (GRNs) with time-varying discrete delays and unbounded distributed delays is considered. So far, there are very few results concerning the problem; and in which the nonnegativity of equilibrium points is neglected. In this paper, the existence of nonnegative equilibrium points is firstly presented. Then, by using the nonsingular M-matrix theory and the functional differential equation theory, M-matrix-based sufficient conditions are proposed to guarantee that the kind of GRNs under consideration here has a unique nonnegative equilibrium point which is globally asymptotically stable. The M-matrix-based stability criteria derived here can be easily verified, since they are to check whether a constant matrix is a nonsingular M-matrix. Several numerical examples are offered to illustrate the effectiveness of the approach proposed in this paper. (C) 2015 Elsevier B.V. All rights reserved.
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