Stability and Bifurcation in a Neural Network Model with Two Delays

Recently, a large number of neural networks models have been proposed and studied extensively since Hopfield constructed a simplified neural network. In most networks however, it is usually expected that time delays exist during the processing and transmission of signals. In general, delay-differential equations exhibit much more complicated dynamics than ordinary differential equations since a time delay could cause a stable equilibrium to become unstable [1]. Recently, time delays have been incorporated into neural network models by many authors [1, 2, 4, 5, 6], there has been great interest in dynamical characteristics of neural network model with delay. In present paper, we consider a simplified Hopfield-type neural network model with two delays { u̇1 (t) = −u1(t) + a11f(u1(t)) + a12f(u2(t− τ1)), u̇2 (t) = −u2(t) + a21f(u1(t− τ2)) + a22f(u2(t)), (1)