Synchronization of chaotic neural networks via output or state coupling

We consider the problem of global exponential synchronization between two identical chaotic neural networks that are linearly and unidirectionally coupled. We formulate a general framework for the synchronization problem in which one chaotic neural network, working as the driving system (or master), sends its output or state values to the other, which serves as the response system (or slave). We use Lyapunov functions to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global exponential synchronization regardless of their initial states. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.