Some properties of the attractors of discrete‐time cellular neural networks
R. Perfetti · International Journal of Circuit Theory and Applications · 1995
Abstract Some theoretical properties concerning discrete‐time (discrete‐state) cellular neural networks (DTCNNs) are presented which illustrate the role of self‐feedback and shed some light on the sizes and shapes of the attraction basins. the main results proved in the paper are the following. (1) With no self‐feedback, two states cannot both be fixed points of the DTCNN dynamics if they differ or coincide in isolated grid positions. (2) With no self‐feedback, every state which differs from a fixed point v (coincides with v) only in isolated grid positions is attracted to v(‐v) along some orbit with block‐sequential dynamics. (3) For a k‐attractor of a DTCNN we have k < (2r + 1)2/2, where r is the neighbourhood radius. (4) the attraction domain of a k‐attractor v includes all the states which differ from v in at most k positions per neighbourhood. the properties proved herein are a consequence exclusively of the local connectivity of DTCNNs.