Stability Analysis of Discrete Hopfield Neural Networks with the Nonnegative Definite Monotone Increasing Weight Function Matrix

The original Hopfield neural networks model is adapted so that the weights of the resulting network are time varying. In this paper, the Discrete Hopfield neural networks with weight function matrix DHNNWFM the weight changes with time, are considered, and the stability of DHNNWFM is analyzed. Combined with the Lyapunov function, we obtain some important results that if weight function matrix WFM is weakly or strongly nonnegative definite function matrix, the DHNNWFM will converge to a stable state in serial or parallel model, and if WFM consisted of strongly nonnegative definite function matrix and column or row diagonally dominant function matrix, DHNNWFMwill converge to a stable state in parallel model.