Configurations of steady states for Hopfield-type neural networks

The dependence of the steady states on the external input vector I for the continuous-time and discrete-time Hopfield-type neural networks of n neurons is discussed. Conditions for the existence of one or several paths of steady states are derived. It is shown that, in some conditions, for an external input I there may exist at least 2n exponentially stable steady states (called configuration of steady states), and their regions of attraction are estimated. This means that there exist 2n paths of exponentially stable steady states defined on a certain set of input values. Conditions assuring the transfer of a configuration of exponentially stable steady states to another configuration of exponentially stable steady states by successive changes of the external input are obtained. These results may be important for the design and maneuvering of Hopfield-type neural networks used to analyze associative memories.