Global exponential stability in Hopfield and bidirectional associative memory neural networks with time delays (Q1884132)

The authors consider a variant of the Hopfield neural network \[ \frac{du_i}{dt} = -d_i u_i + \sum_{j=1}^N b_{ij} g_j(u_j(t-\tau_j))+ I_i, \quad i=1,\dots,n. \] The first result concerns the existence and uniqueness of an equilibrium. Then, using a Lyapunov functional, sufficient conditions for the global exponential stability are obtained. Finally, a bidirectional associative memory neural network is studied.