Stability Of Three Kinds Of Time-delayed Reaction-diffusion Neural Network Models

The dynamics of neural network is a kind of special structure systems. In recentyears, neural network has been closely combined with many disciplines, and manydifferent types of neural network models occur. Therefore, in this thesis we mainlystudy stability of the following three neural network models.In Section2, by using the properties of M-cone, theory of the spectral radius ofnonnegative matrices, Lyapunov functional, Ito formula and inequality techniques,the problem of the exponential stability for a class of impulsive stochastic fuzzy cellularneural networks with distributed delays and reaction-diffusion terms is investigated.In Section3, this thesis is devoted to investigating the robust stochastic exponentialstability for reaction-diffusion Cohen-Grossberg neural networks (RDCGNNs) withMarkovian jumping parameters and mixed delays. By employing a Lyapunov functional,the Ito formula of stochastic differential equation and some differential inequalities,some criteria for delay-dependent robust exponential stability of RDCGNNs withMarkovian jumping parameters are established in terms of linear matrix inequalities.In Section4, this thesis is devoted to investigating the robust stochastic exponentialstability for reaction-diffusion neural networks (RDNNs) with Markovian jumpingparameters and mixed delays. Similarly, some criteria for delay-dependent robustexponential stability of RDNNs with Markovian jumping parameters are established interms of linear matrix inequalities.Besides, examples are provided to illustrate the validity of the theorems in thethesis.