{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T15:25:29Z","timestamp":1740151529181,"version":"3.37.3"},"reference-count":28,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,12,31]],"date-time":"2012-12-31T00:00:00Z","timestamp":1356912000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004055","name":"King Fahd University of Petroleum and Minerals","doi-asserted-by":"publisher","award":["IN111052"],"award-info":[{"award-number":["IN111052"]}],"id":[{"id":"10.13039\/501100004055","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Artificial Neural Systems"],"published-print":{"date-parts":[[2012,12,31]]},"abstract":"<jats:p>For the Hopfield Neural Network problem we consider unbounded monotone nondecreasing activation functions. We prove convergence to zero in an exponential manner provided that we start with sufficiently small initial data.<\/jats:p>","DOI":"10.1155\/2012\/571358","type":"journal-article","created":{"date-parts":[[2012,12,31]],"date-time":"2012-12-31T21:05:26Z","timestamp":1356987926000},"page":"1-5","source":"Crossref","is-referenced-by-count":3,"title":["Hopfield Neural Networks with Unbounded Monotone Activation Functions"],"prefix":"10.1155","volume":"2012","author":[{"given":"Nasser-eddine","family":"Tatar","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}]}],"member":"311","reference":[{"key":"8","doi-asserted-by":"crossref","first-page":"2554\u2013","DOI":"10.1073\/pnas.79.8.2554","volume":"79","year":"1982","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"9","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1126\/science.3755256","volume":"233","year":"1986","journal-title":"Science"},{"year":"1992","series-title":"Mathematics and Its Applications, East European Series","key":"1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1109\/72.207617"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/31.101272"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(99)00074-X"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2005.852862"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1109\/81.401145"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2008.02.022"},{"key":"11","doi-asserted-by":"crossref","first-page":"4815","DOI":"10.1088\/0305-4470\/29\/16\/008","volume":"29","year":"1996","journal-title":"Journal of Physics A"},{"key":"12","first-page":"554","volume":"35","year":"1998","journal-title":"IEEE Transactions on Circuits and Systems I"},{"key":"15","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.chaos.2006.06.035","volume":"32","year":"2007","journal-title":"Chaos, Solitons & Fractals"},{"key":"16","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1109\/72.914530","volume":"12","year":"2001","journal-title":"IEEE Transactions on Neural Networks"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.07.002"},{"issue":"5","key":"18","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/0893-6080(91)90014-V","volume":"4","year":"1991","journal-title":"Neural Networks"},{"issue":"6","key":"19","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1137\/S0036139997321219","volume":"58","year":"1998","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"23","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.physleta.2004.03.038","volume":"325","year":"2004","journal-title":"Physics Letters A"},{"issue":"4","key":"24","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/72.508925","volume":"7","year":"1996","journal-title":"IEEE Transactions on Neural Networks"},{"key":"25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-247X(84)90151-3","volume":"103","year":"1984","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"26","first-page":"1","volume":"68","year":"2003","journal-title":"Physical Review E"},{"year":"1991","key":"13"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(01)00088-0"},{"key":"27","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0893-6080(03)00077-7","volume":"17","year":"2004","journal-title":"Neural Networks"},{"key":"28","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1016\/j.apm.2008.02.006","volume":"33","year":"2009","journal-title":"Applied Mathematical Modelling"},{"key":"20","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1016\/j.nonrwa.2008.04.016","volume":"10","year":"2009","journal-title":"Nonlinear Analysis: Real World Applications"},{"key":"21","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s11071-010-9926-9","volume":"66","year":"2011","journal-title":"Nonlinear Dynamics"},{"key":"22","doi-asserted-by":"crossref","first-page":"2347","DOI":"10.1016\/j.apm.2007.09.002","volume":"32","year":"2008","journal-title":"Applied Mathematical Modelling"},{"volume":"55","volume-title":"Differential and integral inequalities: theory and applications","year":"1969","key":"14"}],"container-title":["Advances in Artificial Neural Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/571358.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/571358.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2012\/571358.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T04:38:39Z","timestamp":1607575119000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/aans\/2012\/571358\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,31]]},"references-count":28,"alternative-id":["571358","571358"],"URL":"https:\/\/doi.org\/10.1155\/2012\/571358","relation":{},"ISSN":["1687-7594","1687-7608"],"issn-type":[{"type":"print","value":"1687-7594"},{"type":"electronic","value":"1687-7608"}],"subject":[],"published":{"date-parts":[[2012,12,31]]}}}