Abstract: Without assuming the boundedness, continuous, derivation of the active functions and the boundedness of the mean time-delay, the existence of a class of neural networks’ periodic solution involving distributed delays with periodic inputs is obtained by using the theory of coincidence degree and the knowledge of Dini derivative, when the active functions satisfy the Lipchitz condition and the relations of the interconnection matrix is an M-matrix.
Meanwhile, under the same conditions, the global exponential stability of neural networks’ periodic solution is obtained by employing Dini derivative and the analysis technique of inequality. Some existing conclusions are improved, extended and complemented. An example is also worked out to demonstrate the advantages of these results.

Key words: Neural network, Periodic solution, Continuously distributed time-delay, Global exponential stability.