{"id":"https://openalex.org/W2994669789","doi":"https://doi.org/10.1080/00207160.2019.1704740","title":"Coexistence of multiple continuous attractors for lower-ordered neural networks","display_name":"Coexistence of multiple continuous attractors for lower-ordered neural networks","publication_year":2019,"publication_date":"2019-12-16","ids":{"openalex":"https://openalex.org/W2994669789","doi":"https://doi.org/10.1080/00207160.2019.1704740","mag":"2994669789"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2019.1704740","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1704740","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-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/A5053249843","display_name":"Jiali Yu","orcid":"https://orcid.org/0000-0002-5895-0805"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiali Yu","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-5895-0805","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030837786","display_name":"Xiong Dai","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiong Dai","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037532475","display_name":"Wenshuang Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenshuang Chen","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100769675","display_name":"Chunxiao Wang","orcid":"https://orcid.org/0000-0002-8387-5923"},"institutions":[{"id":"https://openalex.org/I44445938","display_name":"Shandong Jianzhu University","ror":"https://ror.org/01gbfax37","country_code":"CN","type":"education","lineage":["https://openalex.org/I44445938"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunxiao Wang","raw_affiliation_strings":["School of Science, Shandong Jianzhu University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-8387-5923","affiliations":[{"raw_affiliation_string":"School of Science, Shandong Jianzhu University, Jinan, China","institution_ids":["https://openalex.org/I44445938"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101774864","display_name":"Jin Qi","orcid":"https://orcid.org/0000-0001-8427-0080"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Qi","raw_affiliation_strings":["School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053249843"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":null,"apc_paid":null,"fwci":0.1777,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.5662507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"97","issue":"12","first_page":"2462","last_page":"2473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10320","display_name":"Neural Networks and Applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.9462085962295532},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6375155448913574},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6179463267326355},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6119550466537476},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5273911356925964},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4292791485786438},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4274135231971741},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.413601815700531},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3636817932128906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3075994849205017},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28685900568962097},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11404162645339966},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10891395807266235},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07658454775810242}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.9462085962295532},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6375155448913574},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6179463267326355},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6119550466537476},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5273911356925964},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4292791485786438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4274135231971741},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.413601815700531},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3636817932128906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3075994849205017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28685900568962097},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11404162645339966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10891395807266235},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07658454775810242},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2019.1704740","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1704740","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3500669590","display_name":null,"funder_award_id":"61572112, 61103041, 11271001, 61370147, 61803228","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4041772958","display_name":null,"funder_award_id":"2019YJ0185","funder_id":"https://openalex.org/F4320322922","funder_display_name":"Department of Science and Technology of Sichuan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322922","display_name":"Department of Science and Technology of Sichuan Province","ror":"https://ror.org/04323m874"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1578196132","https://openalex.org/W1608745771","https://openalex.org/W2023739945","https://openalex.org/W2036958054","https://openalex.org/W2097671547","https://openalex.org/W2112246162","https://openalex.org/W2125805354","https://openalex.org/W2129481537","https://openalex.org/W2130837362","https://openalex.org/W2131659116","https://openalex.org/W2134114905","https://openalex.org/W2137700545","https://openalex.org/W2157518752","https://openalex.org/W2167809052","https://openalex.org/W2298027766","https://openalex.org/W2344296589","https://openalex.org/W2462610458","https://openalex.org/W2556852084","https://openalex.org/W2564041812","https://openalex.org/W2610437157","https://openalex.org/W2766554021","https://openalex.org/W2810135222","https://openalex.org/W2911458328","https://openalex.org/W2916328840","https://openalex.org/W2969226653","https://openalex.org/W6601258158"],"related_works":["https://openalex.org/W3083820578","https://openalex.org/W2087814933","https://openalex.org/W2031094851","https://openalex.org/W2044927803","https://openalex.org/W1982496263","https://openalex.org/W2033504252","https://openalex.org/W2751190634","https://openalex.org/W2010923533","https://openalex.org/W2155185845","https://openalex.org/W2088255893"],"abstract_inverted_index":{"A":[0,25],"continuous":[1,36,43,57],"attractor":[2],"of":[3,11,22,28,55,75],"recurrent":[4],"neural":[5,47],"network":[6,60],"is":[7,49],"a":[8,20],"connected":[9],"set":[10],"stable":[12],"equilibrium":[13],"points.":[14],"It's":[15],"widely":[16],"used":[17],"to":[18],"interpret":[19],"lot":[21],"brain":[23],"activities.":[24],"large":[26],"number":[27],"literatures":[29],"have":[30],"studied":[31,50],"discrete":[32],"attractors":[33,44,58],"and":[34,51,62],"single":[35],"attractor.":[37],"In":[38],"this":[39],"paper,":[40],"the":[41,52,73,76,80],"coexisting":[42,53],"for":[45,59],"nonlinear":[46],"networks":[48],"conditions":[54],"two":[56],"with":[61],"without":[63],"external":[64],"input":[65],"in":[66],"two-dimensional":[67],"space":[68],"are":[69,82],"obtained":[70],"by":[71,84],"analysing":[72],"eigenvalues":[74],"matrix.":[77],"Finally,":[78],"all":[79],"results":[81],"verified":[83],"simulation.":[85]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
