Research Of Stability For The Stochastic Genetic Regulatory Networks Model

Gene regulatory network(GRNs)is a kind of dynamic system which describe the relationship between genes(mRNA)and protein.Because GRNs plays a key role in cell biology,it gets more and more attention in the field of mathematical biology.In this paper,we set up and study two types of gene regulation network models to study the dynamic behavior of the GNS.The following are the main research contents of this paper :Firstly,a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks(GRNs)with time-varying delays and reaction-diffusion driven by fractional Brownian motion(fBm)is present.By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient condition for the exponential stability of the stochastic model of impulsive GRN in the mean-square sense.An example is presented to illustrate our results of the mean-square exponential stability analysis.Secondly,we conduct a dissipative analysis for comprehensive genetic regulatorynetwork models withfractional Brownian motion(fBm),diffusion-reaction processes,Markovian jump and time-varying delay.By constructing an appropriate Lyapunov–Krasovskii functional,utilizing linear matrix inequality(LMI)technique and stochastictheory,a sufficient conditions of global dissipativity and strictly(Q,S,R)--dissipativity of the solution are established.Moreover,the global attractive sets which are positive invariant are obtained.