{"id":"https://openalex.org/W2018754379","doi":"https://doi.org/10.1109/ijcnn.2012.6252549","title":"Continuous attractors of recurrent neural networks with complex-valued weights","display_name":"Continuous attractors of recurrent neural networks with complex-valued weights","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2018754379","doi":"https://doi.org/10.1109/ijcnn.2012.6252549","mag":"2018754379"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2012.6252549","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2012.6252549","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 2012 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100691319","display_name":"Jun Li","orcid":"https://orcid.org/0000-0002-6239-2922"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Li","raw_affiliation_strings":["School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China","School of Computer Science and Technology, Nanjing University of Science and Technology, China, 210094"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]},{"raw_affiliation_string":"School of Computer Science and Technology, Nanjing University of Science and Technology, China, 210094","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100726984","display_name":"Jian Yang","orcid":"https://orcid.org/0000-0003-4800-832X"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Yang","raw_affiliation_strings":["School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China","School of Computer Science and Technology, Nanjing University of Science and Technology, China, 210094"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]},{"raw_affiliation_string":"School of Computer Science and Technology, Nanjing University of Science and Technology, China, 210094","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yongfeng Diao","orcid":null},"institutions":[{"id":"https://openalex.org/I16351329","display_name":"China West Normal University","ror":"https://ror.org/04s99y476","country_code":"CN","type":"education","lineage":["https://openalex.org/I16351329"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongfeng Diao","raw_affiliation_strings":["School of Computer Science and Technology, China West Normal University, Nanchong, China","School of Computer Science and Technology, China West Normal University, Nanchong, China 637002"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, China West Normal University, Nanchong, China","institution_ids":["https://openalex.org/I16351329"]},{"raw_affiliation_string":"School of Computer Science and Technology, China West Normal University, Nanchong, China 637002","institution_ids":["https://openalex.org/I16351329"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100691319"],"corresponding_institution_ids":["https://openalex.org/I36399199"],"apc_list":null,"apc_paid":null,"fwci":0.7451,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73169476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"353","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.8827502727508545},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.832601010799408},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.8072059154510498},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.6483619809150696},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5728551149368286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43853744864463806},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41361963748931885},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4047549068927765},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.39240002632141113},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19337144494056702},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16841119527816772},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11489707231521606},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.07146519422531128},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.058756113052368164},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.05612218379974365}],"concepts":[{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.8827502727508545},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.832601010799408},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8072059154510498},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6483619809150696},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5728551149368286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43853744864463806},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41361963748931885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4047549068927765},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.39240002632141113},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19337144494056702},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16841119527816772},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11489707231521606},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.07146519422531128},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.058756113052368164},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.05612218379974365},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2012.6252549","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2012.6252549","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 2012 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1481099253","https://openalex.org/W1516351231","https://openalex.org/W1585539754","https://openalex.org/W1993545737","https://openalex.org/W2029689911","https://openalex.org/W2071410910","https://openalex.org/W2074540734","https://openalex.org/W2075885336","https://openalex.org/W2097671547","https://openalex.org/W2105239794","https://openalex.org/W2107734128","https://openalex.org/W2108550895","https://openalex.org/W2118580492","https://openalex.org/W2119481995","https://openalex.org/W2125805354","https://openalex.org/W2130929719","https://openalex.org/W2131659116","https://openalex.org/W2134671148","https://openalex.org/W2135860340","https://openalex.org/W2157518752","https://openalex.org/W2158189881","https://openalex.org/W2161758637","https://openalex.org/W2161780063","https://openalex.org/W2169006540","https://openalex.org/W2175497113","https://openalex.org/W3124629440"],"related_works":["https://openalex.org/W4251428025","https://openalex.org/W3049714198","https://openalex.org/W2960434112","https://openalex.org/W2036805113","https://openalex.org/W2784467519","https://openalex.org/W4289867043","https://openalex.org/W2592279130","https://openalex.org/W2049158118","https://openalex.org/W2123827981","https://openalex.org/W4205994410"],"abstract_inverted_index":{"The":[0],"global":[1,5],"exponential":[2],"stability":[3,7],"(GAS),":[4],"asymptotic":[6],"(GES)":[8],"and":[9],"multi-stability":[10],"(MS)":[11],"continuous":[12,29,61,71],"attractors":[13,62,72],"of":[14,63,73],"recurrent":[15],"neural":[16],"networks":[17],"(RNN)":[18],"with":[19,65,75,85],"complex-valued":[20,76],"weights":[21,67,77],"are":[22,68,78,90],"studied":[23],"in":[24],"this":[25],"paper.":[26],"As":[27],"a":[28,47],"attractor":[30],"is":[31,44],"the":[32,35,57,82,96],"infinite":[33],"equilibria,":[34],"connected":[36],"matrix":[37],"needs":[38],"to":[39,94],"be":[40],"nonsingular.":[41],"Therefore,":[42],"RNN":[43,50,64,74,84],"transformed":[45],"into":[46],"lower":[48],"dimensional":[49],"using":[51],"elementary":[52],"operation.":[53],"Firstly,":[54],"based":[55],"on":[56],"foregoing":[58],"results":[59],"some":[60],"real-valued":[66,86],"obtained.":[69],"Secondly,":[70],"obtained":[79],"by":[80],"studying":[81],"corresponding":[83],"weights.":[87],"Some":[88],"simulations":[89],"finally":[91],"carried":[92],"out":[93],"illustrate":[95],"theory.":[97]},"counts_by_year":[{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}