Neural networks (NNs), especially Hopfield neural networks, Cellular neural networks (CNNs), Cohen-Gross berg neural networks (CGNNs), Bidirectional associative memory (BAM) neural networks, and these networks with time delays, have been deeply investigated in recent years due to their potential applications in the areas of signal and image processing, associative memories and pattern classification, parallel computation and optimization problems. In the design of NNs, the dynamics of networks such as the existence-uniqueness and global asymptotic stability or global exponential stability of equilibrium points of the networks play an important role. For example, in solving optimization problems, the neural network must be designed to have one unique and globally stable equilibrium point. In the analysis of parallel computation, to increase the rate of convergence to the equilibrium point of the networks and reduce the neural computing time, it is necessary to ensure a desired exponential convergence rate of the networks’ trajectories, starting from arbitrary initial states to the equilibrium point which corresponds to the optimal solution, and so there is a strong motivation to study the global (exponential) stability of equilibrium points for neural networks.

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