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Sufficient conditions are obtained for the existence and uniqueness of the equilibrium point for the addressed neural networks.<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>th moment exponential stability is investigated by means of Lyapunov functional, stochastic analysis, and inequality technique. The results in this paper improve and generalize some of the previous ones. 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