Stability Of Fuzzy BAM Neural Networks

The bi-directional associative memory (BAM) neural networks were introduced by Kosko in 1987, these models generalized the single-layer autoassociative to a two-layer pattern-matched heteroassociative circuits. The class of networks has wide applications in many fields such as pattern recognition, associative memory and artificial intelligence. Such model caused much attention of researchers.Since T. Yang and L. B. Yang proposed another type-fuzzy cellular networks (FCNN) in 1996, which integrated fuzzy logic into the structure of cellular neural networks (CNN). FCNN has fuzzy logic between its template input and output, which unlike tradition CNN. It retains the characteristics of the traditional model and the local connections between cells, to facilitate the stability of neural networks. The model adds new features as the connection of the traditional model. Recently the stability of fuzzy neural networks has aroused great interest of researchers.In fact, it is impossible to avoid the delays in neural networks because of various reasons. It may cause the unstability or disturbing of the neural networks due to the delays. So it is important to research the dynamical behaviors of neural networks with delays. However, strictly speaking, diffusion effects cannot be avoided in the neural networks when electrons are moving in asymmetric electromagnetic fields. So it is also studied the stability of the neural networks with reaction-diffusion terms in this thesis.To the best of our knowledge, there exist few results on the stability of fuzzy BAM neural networks. It improved another researchers'pattern in this thesis. And some sufficient conditions for the uniqueness and exponential stability, global exponential stability and global asymptotic stability of equilibrium points are obtained.This thesis is concerned with the stability of fuzzy BAM neural networks. This thesis is organized as follows:Chapter 1 introduces the background, research status of this issue, the content and the main results of this thesis.Chapter 2 introduces exponential stability of a class of fuzzy BAM neural networks with distributed delays, some sufficient conditions ensuring existence uniqueness and exponential stability of equilibrium point, which makes use of contraction mapping principle, Lyapunov functional and the nature of the activation functions. An example is given to demonstrate the effectiveness of the obtained results.Chapter 3 introduces global exponential stability of a class of fuzzy BAM neural networks with variable delays. By using the fixed point theorem, Halanay-type inequalities. A delay-independent sufficient condition for equilibrium point is obtained. A numerical example is given to illustrate the effectiveness of the results we have obstained.Chapter 4 introduces global asymptotic stability of a class of fuzzy BAM neural networks with distributed delays and reaction-diffusion terms. A sufficient condition is obtained by using the Lyapunov functional and the analysis technique. A numerical example is given to show the effectiveness of our analysis.