Dynamics of some neural network models with delay.

The dynamics of the neuronic model described by the one-dimensional delay functional differential equation are studied in this paper. We give a strict and detailed analysis of dynamical characteristic of this model by the Lyapunov functional approach and Hopf bifurcation proposition. Furthermore, numerical simulations, as well as Lyapunov exponents, are presented to support our conjectures about the appearance of complex dynamics such as chaos. We also investigate the dynamics of the neural network model described by the n-dimensional delay functional differential equation with a symmetrical weight matrix, and corresponding simulation results are included as concrete examples.