Global existence of periodic solutions in a special neural network model with two delays

A simple neural network model with two delays is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when file sum of two delays passes through a sequence of critical values. Using a global Hopf bifurcation theorem for FDE due to Wu [Wu J. Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 1998;350:4799-838], a group of sufficient conditions for this model to have multiple periodic solutions are obtained when the sum of delay's is sufficiently large. Numerical simulations are presented to support the obtained theoretical results. (c) 2007 Elsevier Ltd. All rights reserved.