Journal
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS
Volume 28, Issue 4, Pages 841-864Publisher
SPRINGER INDIA
DOI: 10.1007/s12591-017-0349-7
Keywords
Stochastic genetic regulatory networks; Reaction-diffusion; Dissipativity; Linear matrix inequality (LMI); Fractional Brownian motion (fBm)
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Funding
- National Science Foundation of China [11461053, 11661054]
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This paper conducts a dissipative analysis for comprehensive genetic regulatory network models with fractional Brownian motion (fBm), diffusion-reaction processes, Markovian jump and time-varying delay. By constructing an appropriate LyapunovKrasovskii functional, utilizing linear matrix inequality (LMI) technique and stochastic theory, several sufficient conditions of global dissipativity and strictly (Q, S, R)-gamma-dissipativity of the solution are established. Moreover, the global attractive sets which are positive invariant are obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.
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