Locally Asymptotically Stable Fixed-point Assignment Problems in Neural Networks and Application to Associative Memory

This paper proposes and studies in the frame work of systems and control theory the problem of how to construct a dynamical system defined over a Hilbert space such a way that any given vectors are assigned to locally asymptotically stable fixed-points of the system. Some basic properties of such systems are investigated, and further the results are applied to neural networks to implement associative memory or pattern recognition for two-dimensional images in such a way that a certain structural deformation of images is acceptable. Finally some numerical examples for associative memory are presented to illustrate the performance.