In this paper, we consider a delayed network of two neurons with self-feedback and interaction described by an all-or-none threshold function.The discontinuity of signal function makes it di4cult to apply directly dynamical system.We show that the dynamics of the network can be understood in terms of the iterations of a one-dimensional map, and we obtain the existence and attractivity of periodic solutions.Moreover, because the network is a limiting case of the corresponding smooth system as the parameter tends to in7nity, the above results can act as the guide to the rich dynamics of the smooth system.Therefore, our results have important signi7cance in both theory and plications. © 2003 Elsevier B.V. All rights reserved.

In this paper we study a class of neural networks with continuously distributed delays. By means the of yapunov functional method, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution. We also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified. Therefore, our results play an important role in the design of globally exponentially stable neural circuits and periodic oscillatory neural circuits.