Matrix Criterion for Dynamic Analysis in Discrete Neural Networks with Delay

The dynamics of discrete neural network with delay are studied in this paper using a matrixinequality which is shown to be equivalent to the state transition equation of the network. For the network witharbitrary weight matrix, the conditions for the existence of cycle of length 1 and 2 are presented. Also, theconditions for the existence of special cycle of length l, 2 and 4, for having no any stable states are achieved.Computer simulations demonstrate that the theoretical analysis is correct.