{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T05:19:27Z","timestamp":1695791967583},"reference-count":10,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,12,15]],"date-time":"2006-12-15T00:00:00Z","timestamp":1166140800000},"content-version":"vor","delay-in-days":4123,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory &amp; Apps"],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Some theoretical properties concerning discrete\u2010time (discrete\u2010state) cellular neural networks (DTCNNs) are presented which illustrate the role of self\u2010feedback 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\u2010feedback, two states cannot both be fixed points of the DTCNN dynamics if they differ or coincide in isolated grid positions. (2) With no self\u2010feedback, every state which differs from a fixed point v (coincides with v) only in isolated grid positions is attracted to v(\u2010v) along some orbit with block\u2010sequential dynamics. (3) For a <jats:italic>k<\/jats:italic>\u2010attractor of a DTCNN we have <jats:italic>k<\/jats:italic> &lt; (2<jats:italic>r<\/jats:italic> + 1)<jats:sup>2<\/jats:sup>\/2, where <jats:italic>r<\/jats:italic> is the neighbourhood radius. (4) the attraction domain of a <jats:italic>k<\/jats:italic>\u2010attractor v includes all the states which differ from v in <jats:italic>at most<\/jats:italic> k <jats:italic>positions per neighbourhood<\/jats:italic>. the properties proved herein are a consequence exclusively of the local connectivity of DTCNNs.<\/jats:p>","DOI":"10.1002\/cta.4490230503","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T14:16:24Z","timestamp":1183385784000},"page":"485-499","source":"Crossref","is-referenced-by-count":4,"title":["Some properties of the attractors of discrete\u2010time cellular neural networks"],"prefix":"10.1002","volume":"23","author":[{"given":"R.","family":"Perfetti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,12,15]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1982.12424"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1982.12428"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1986.1165005"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/29.56021"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/29.90388"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/29.17533"},{"key":"e_1_2_1_8_2","unstructured":"M. F.Fahmy G. M.El\u2010RaheemandR. R.Gharieb \u2018IIR adaptive filters using discrete orthogonal functions\u2019 Proc. IEEE Symp. on Circuits and System San Diego CA May 1992 pp.2902\u20132905 New York 1992."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490210402"},{"key":"e_1_2_1_10_2","first-page":"126","article-title":"Channel equalization using discrete orthogonal functions","volume":"6","author":"El\u2010Raheem G. M.","year":"1994","journal-title":"Bull. Fac. Eng., Assiut Univ."},{"key":"e_1_2_1_11_2","volume-title":"Adaptive Filter Theory","author":"Haykin S.","year":"1991"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.4490230503","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.4490230503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T09:57:28Z","timestamp":1695722248000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.4490230503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1002\/cta.4490230503"],"URL":"https:\/\/doi.org\/10.1002\/cta.4490230503","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}