Dynamic Analysis Of Recurrent Neural Networks

Recurrent neural networks are widely used in pattern recognition, image processing, intelligent control, signal processing, optimistic computation, etc. It is well known that such kinds of these applications rely crucially on qualitative properties of the dynamic behaviors of recurrent neural networks.Consequently, the study of the dynamical behaviors of recurrent neural networks has important theoretical and practical significance. This dissertation mainly focuses on the stability of equilibrium point, the existence and the stability of periodic solution. Our investigations are based on Lyapunov functional theory, M matrix theory, linear matrix inequalities and fixed point theorem. The main contents of this dissertation are shown as follows:Based on Lyapunov functional theory, Schur complement lemma and It? differential formula, we obtain some sufficient criteria ensuring the mean square exponential stability of equilibrium point of stochastic interval neural networks with mixed time delays. The criteria are derived in terms of linear matrix inequalities, which can be easily solved by the Matlab LMI toolbox, and no tuning of parameters is required. Moreover, the obtained results are superior to the existing ones in the previous literatures.Numerical examples are provided to show the usefulness of these criteria.There are some BAM neural networks can not be appropriately described by pure continuous or pure discrete equations for abrupt changes at certain moments. Therefore, a class of BAM neural networks is considered. In terms of homeomorphism, Young inequality, H?lder inequality and reduction to absurdity, we obtain the sufficient conditions of the existence and uniqueness of the equilibrium without assuming the boundedness and differentiability of the activation functions. Based on M matrix theory and reduction to absurdity, we give some sufficient criteria ensuring the global exponential stability of the equilibrium point. By utilizing Lyapunov functional theory, linear matrix inequality technique and fixed point theorem, the sufficient criteria ensuring the existence and global exponential stability of the periodic solutions for the high-order BAM neural network with impulses and time delays are obtained. The criteria are derived in M matrix. Moreover, the obtained results are superior to the existing ones in the previous literatures.Numerical examples are provided to show the usefulness of these criteria.The global exponential stability of impulsive neural networks with mixed time delays is discussed in this dissertation. Based on Lyapunov functional theory and linear matrix inequality technique, delay dependent stability criteria are obtained in terms of linear matrix inequalities, which can be easily solved by the Matlab LMI toolbox, and no tuning of parameters is required. A numerical example is provided to illustrate the effectiveness of our results. In terms of M matrix theory, linear matrix inequality technique and Lyapunov functionals, we obtain the sufficient conditions of the global exponential stability of fuzzy BAM neural networks without assuming the boundedness and differentiability of the activation functions. The criteria are derived in terms of M matrix. Moreover, the obtained results are superior to the existing ones in the previous literatures.