A discrete Lyapunov system as an efficient associative memory

A discrete Lyapunov system that functions essentially like the Hopfield model (i.e. with feedback and thresholding) is developed. When expanded into a binomial series, the energy function for the discrete Lyapunov system is shown to be approximately equal to the energy function of the Hopfield model and also of models that utilize higher order discriminant functions. The discrete Lyapunov system is used to develop its continuous counterpart by utilizing a differential equation very similar to the one used for the Hopfield continuous model of neurons with graded response.<>