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Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays. (English) Zbl 1216.34080

Summary: The stability analysis problem is investigated for a class of genetic regulatory networks (GRNs) with Markovian jumps and mixed time delays (discrete time delays and distributed time delays) and stochastic perturbations. The main purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable. By utilizing a more general Lyapunov-Krasovskii functional based on the idea of “delay decomposing” and the LMI (linear matrix inequality) technique, we derive sufficient delay-dependent conditions ensuring the asymptotical stability of the GRNs with mixed time delays and noise perturbations in terms of LMI. Finally, simulation examples are exploited to illustrate the effectiveness of the developed theoretical results.

MSC:

34K50 Stochastic functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
92D10 Genetics and epigenetics
92C42 Systems biology, networks
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