Stability Analysis Of Reaction Diffusion Neural Networks With Time Delay

Artificial recurrent neural networks are a very active research area in these years. Recurrent neural networks can be divided into two types according to the difference of basic variables: local field neural network and static neural network, however, most current researches about recurrent neural networks focused on the local field models, little about the static ones, not to mention the static neural networks with reaction-diffusion terms. However, static models are widely reprehensive. Many useful neural networks are modeled as static models. In this paper, we will investigate the global robust stability of static neural networks with reaction-diffusion terms and absolutely exponential stability of local field neural networks. Precisely, four problems are considered:1. global robust stability of static neural networks with time-varying delays and reaction-diffusion terms2. global robust exponential stability of static neural networks with distributed delays and reaction-diffusion terms3. absolutely exponential stability of local field neural networks with time-varying delays and reaction-diffusion terms4. absolutely exponential stability of local field neural networks with distributed delays and reaction-diffusion termsThe paper is divided into four parts:The background of neural networks and mathematical knowledge needed are introduced in Section 1.In Section 2, global robust stability of static neural networks with time-varying delays and reaction-diffusion terms is firstly investigated, and then global robust exponential stability of static neural networks with distributed delays and reaction-diffusion terms is considered with the similar method, the existence of equilibrium is proved by using topology degree and then we obtain a sufficient condition for the uniqueness and global robust stability by constructing a suitable Lyapunov function and inequation estimation. Finally, two examples are given to illustrate the results.In Section 3, absolutely exponential stability of local field neural networks with time-varying delays and reaction-diffusion terms is investigated, an sufficient and necessary condition is obtained to guarantee the existence of equilibrium and absolutely exponential stability, then the model with distributed delays is considered by the same results. Finally a numerical example is given to shown the results.The conclusion of this paper and problems should be investigated are given in Section 4.