Dynamics Behaviors For A Class Of Bi-directional Associative Memory Neural Network

Because the neural network itself has many advantages such as nonlinear mapping abilities, self-organization and self-learning abilities, associative memory capacity, parallel information processing manner and its good fault tolerant abilities, neural networks are widely and successfully applied in pattern recognition, image and voice signal processing, artificial intelligence control and other areas. In the specific application of neural networks, people always hope that neural networks have globally extremely fast convergence properties, large global mapping and generalization approximation abilities, less implementation cost.In this paper a class of Cohen-Grossberg type bi-directional associative memory (BAM) neural network model with time-varying delays and continuous distributed delays is studied. Assuming the Lipschitz conditions of the activation function, the existence and global exponential stability of equilibrium point and periodic solutions of this neural network, the estimation on exponential convergence rate of simplified model are investigated. At the same time, the Hopf bifurcation of a simplified model is discussed. The paper consists of five chapters.In Chapter I, the current advance of study on the BAM neural network model and Cohen-Grossberg neural network is given. The BAM neural models as well as the existing research methods are discussed in detail.In Chapter II, the existence and uniqueness and the global exponential stability of the equilibrium point for the Cohen-Grossberg type BAM neural networks with time-varying delays and continuously distributed delays are investigated. The existence of equilibrium point is analyzed via contraction mapping principle. And the analysis of exponential stability is divided into two cases according to the character of delays and the proper Lyapunov-Krasovskii functionals are constructed respectively. So the uniform condition is derived. The conditions in this paper extend the conditions for cellular neural networks and Hopfield neural networks.The estimation on exponential convergence rate of BAM neural network in the special form is considered in Chapter III. By applying Lyapunov stability theory and norm inequality, some delay independent and delay dependent conditions are derived. Finally, it is easy to be obtained that exponential convergence rate is decreasing with the increase of delay. In Chapter IV, the existence of periodic solutions is studied via the continuation theorem based on Mawhin coincidence degree theory, the properties of nonsingular M ? matrix, integral inequality analysis. Some sufficient conditions ensuring existence and the global exponential stability of periodic attractor are derived.In Chapter V, the bifurcation on a four-neuron BAM neural network with distributed delays is considered. By choosing the average delay as a bifurcation parameter and applying the linearization theory, the normal form theory and the center manifold theorem, the local stability, Hopf bifurcation and asymptotical stability of periodic solutions are in detail discussed. Also a formula determining the direction of Hopf bifurcation is derived. Finally, numerical simulation results are given to validate the theorem obtained.