Stability Of Uncertain Stochastic Bidirectional Associative Memory Networks With Delays

Recently, some of the reasons, why uncertain stochastic bidirectional associative memory neural networks (BAM) with time, delays and parameter uncertainties have received a great deal of attention of people, are because it has good applications in the area of pattern recognition and artificial intelligence. It is well known that for neural networks with delays, it is rather difficult to analyze their stability properties due to time delays and parameter uncertainties, There are usually two ways to do this. One is to linearize the system near equilibrium, conditions obtained in this way concern the local stability around an equilibrium. Another way is to construct a suitable Lyapunov function for system and then to derive sufficient conditions ensuring stability, this usually involves global stability. In real nervous systems, the synaptic transmission is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes. It has also been known that a neural network could be stabilized or destabilized by certain stochastic inputs. Hence, the stability analysis problem for uncertain stochastic neural networks becomes increasingly significant.This dissertation mainly studies the stability of several classes of uncertain stochastic BAM neural networks with time delays, A series of results are obtained, which of them improve or extend the related results in the literatures, the uncertainties are norm-bounded that enter into all the network parameters. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. Some numerical examples are given to demonstrate the usefulness of the proposed criteria. A set of criteria are proposed for the exponential stability of uncertain stochastic BAM neural networks with time delays, These criteria manifest explicitly the influence of time delay on exponential convergence rate, and the maximal allowable bound of the exponential convergence rate is obtained through using the method of solving the optimization problem. Then the stability property of a class of uncertain stochastic BAM neural networks with time-varying delays is discussed, without assuming the differentiability of the time-varying, only needing that the delays are nonnegative and bounded, the results are less conservative and less restrictive than the ones reported in the literature.. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the stability analysis problem are investigated for a class of stochastic BAM neural networks with mixed time delays and parameter uncertainties. The mixed time delays consist of both the discrete delays and the distributed delays.