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By constructing suitable Lyapunov functions, the authors study the existence, uniqueness and global exponential stability of periodic solution for impulsive Hopfield neural networks with time-varying delays. Their condition extends and generalizes a known condition for the global exponential periodicity of continuous Hopfield neural networks with time-varying delays. Further the numerical simulation shows that their system can occur many forms of complexities including gui strange attractor and periodic solution. In recent years, stability of different classes of neural networks with time delay, such as Hopfield neural networks, cellular neural networks, bidirectional associative neural networks, Lotka-Volterra neural networks, has been extensively studied and various stability conditions have been obtained for these models of neural networks.
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