Abstract: This paper discusses stability of discrete time Hopfield network with the sequential weight which is asymmetry or with the activation function which is non-monotonic. New energy function is imported, then it proved that the energy function of network is declined monotonously with the updating of the state using the properties of convex function, gained the sufficient condition of the network convergence in the end. To the activation function that is non-monotonic sequential function, when product of the maximum characteristic value of the network connecting weight matrix and the infimum of the derivative to the activation function of the nerve cell more than -1, the network convergences concurrently. At the same time, to the network activation function is monotonous sequential function, and the network connecting weight is asymmetry matrix, when the product of the maximum value of derivative to the nerve cell and the matrix of the two-norm to the connecting weight value is less than 1, the network convergences concurrently.
Subgradient of convex function,