Dynamics of Delayed Neural Networks with Impulses

[摘要] 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 inrecent years due to their potential applications in the areas of signaland image processing, associative memories and pattern classification,parallel computation and optimization problems. In the design ofNNs, the dynamics of networks such as the existence-uniqueness andglobal asymptotic stability or global exponential stability of equilibriumpoints of the networks play an important role. For example, in solvingoptimization problems, the neural network must be designed to haveone unique and globally stable equilibrium point. In the analysisof parallel computation, to increase the rate of convergence to theequilibrium point of the networks and reduce the neural computingtime, it is necessary to ensure a desired exponential convergence rateof the networks’ trajectories, starting from arbitrary initial states to theequilibrium point which corresponds to the optimal solution, and sothere is a strong motivation to study the global (exponential) stabilityof equilibrium points for neural networks [1,2].