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Some properties of the attractors of discrete‐time cellular neural networks
Author(s) -
Perfetti R.
Publication year - 1995
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490230503
Subject(s) - attractor , neighbourhood (mathematics) , fixed point , mathematics , discrete time and continuous time , domain (mathematical analysis) , state (computer science) , topology (electrical circuits) , physics , mathematical analysis , control theory (sociology) , computer science , combinatorics , algorithm , artificial intelligence , control (management) , statistics
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 < (2 r + 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.