{"id":"https://openalex.org/W2123827981","doi":"https://doi.org/10.1109/tnn.2009.2032269","title":"Nontrivial Global Attractors in 2-D Multistable Attractor Neural Networks","display_name":"Nontrivial Global Attractors in 2-D Multistable Attractor Neural Networks","publication_year":2009,"publication_date":"2009-10-03","ids":{"openalex":"https://openalex.org/W2123827981","doi":"https://doi.org/10.1109/tnn.2009.2032269","mag":"2123827981","pmid":"https://pubmed.ncbi.nlm.nih.gov/19884069"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2009.2032269","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2009.2032269","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5040299913","display_name":"Lan Zou","orcid":"https://orcid.org/0000-0003-2443-0817"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lan Zou","raw_affiliation_strings":["Departmentof Mathematics, Sichuan University, Chengdu 610064, China. lanzou@yahoo.com.cn","Dept. of Math., Sichuan Univ., Chengdu, China"],"affiliations":[{"raw_affiliation_string":"Departmentof Mathematics, Sichuan University, Chengdu 610064, China. lanzou@yahoo.com.cn","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Dept. of Math., Sichuan Univ., Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111500162","display_name":"Huajin Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I3005327000","display_name":"Institute for Infocomm Research","ror":"https://ror.org/053rfa017","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3005327000","https://openalex.org/I91275662"]},{"id":"https://openalex.org/I115228651","display_name":"Agency for Science, Technology and Research","ror":"https://ror.org/036wvzt09","country_code":"SG","type":"government","lineage":["https://openalex.org/I115228651"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Huajin Tang","raw_affiliation_strings":["Institute of Infocomm Research, Agency for Science, Technology and Research, Singapore","Inst. for Infocomm Res., Agency for Sci., Technol. & Res. (A*STAR), Singapore, Singapore#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Infocomm Research, Agency for Science, Technology and Research, Singapore","institution_ids":["https://openalex.org/I3005327000","https://openalex.org/I115228651"]},{"raw_affiliation_string":"Inst. for Infocomm Res., Agency for Sci., Technol. & Res. (A*STAR), Singapore, Singapore#TAB#","institution_ids":["https://openalex.org/I115228651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025285243","display_name":"Kay Chen Tan","orcid":"https://orcid.org/0000-0002-6802-2463"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"K.C. Tan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore","[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019414664","display_name":"Weinian Zhang","orcid":"https://orcid.org/0000-0002-4566-499X"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weinian Zhang","raw_affiliation_strings":["Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, China","Dept. of Math., Sichuan Univ., Chengdu, China"],"affiliations":[{"raw_affiliation_string":"Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Dept. of Math., Sichuan Univ., Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040299913"],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":null,"apc_paid":null,"fwci":1.8127,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86652124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"11","first_page":"1842","last_page":"1851"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9993000030517578,"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/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.9784185290336609},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6501770615577698},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6290761232376099},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.592033326625824},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.571077823638916},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.40032461285591125},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3696576952934265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35706275701522827},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.237295001745224},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21310549974441528},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15298762917518616},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11700841784477234},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06151345372200012}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.9784185290336609},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6501770615577698},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6290761232376099},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.592033326625824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.571077823638916},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40032461285591125},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3696576952934265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35706275701522827},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.237295001745224},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21310549974441528},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15298762917518616},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11700841784477234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06151345372200012},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008432","descriptor_name":"Mathematical Computing","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008432","descriptor_name":"Mathematical Computing","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008432","descriptor_name":"Mathematical Computing","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D055641","descriptor_name":"Mathematical Concepts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055641","descriptor_name":"Mathematical Concepts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055641","descriptor_name":"Mathematical Concepts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1109/tnn.2009.2032269","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2009.2032269","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},{"id":"pmid:19884069","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19884069","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.724.8474","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.724.8474","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.i2r.a-star.edu.sg/%7Ehtang/TNN09_NontrivialAttractors.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W611428499","https://openalex.org/W1546156674","https://openalex.org/W1557040331","https://openalex.org/W1578196132","https://openalex.org/W1594759473","https://openalex.org/W1603053247","https://openalex.org/W1851248039","https://openalex.org/W1991233288","https://openalex.org/W1993545737","https://openalex.org/W2036958054","https://openalex.org/W2097671547","https://openalex.org/W2123827981","https://openalex.org/W2128084896","https://openalex.org/W2128283823","https://openalex.org/W2128747957","https://openalex.org/W2129481537","https://openalex.org/W2130837362","https://openalex.org/W2134114905","https://openalex.org/W2134683599","https://openalex.org/W2139411083","https://openalex.org/W2144789942","https://openalex.org/W2148830696","https://openalex.org/W2154191582","https://openalex.org/W2155547196","https://openalex.org/W2157518752","https://openalex.org/W2506699060","https://openalex.org/W4292366025"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W154868527","https://openalex.org/W1494268238","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W4291418281","https://openalex.org/W2469703203","https://openalex.org/W2966150910"],"abstract_inverted_index":{"Attractor":[0],"dynamics":[1],"is":[2,12],"a":[3,28,44,92],"crucial":[4],"problem":[5],"for":[6,17],"attractor":[7,31],"neural":[8,23],"networks,":[9],"as":[10],"it":[11,89],"the":[13,49,77,83,106],"underling":[14],"computational":[15],"mechanism":[16],"memory":[18],"storage":[19],"and":[20,38,56,86,88],"retrieval":[21],"in":[22,59],"systems.":[24],"This":[25],"brief":[26],"studies":[27],"class":[29],"of":[30,34,51,79],"network":[32,80],"consisting":[33],"linearized":[35],"threshold":[36],"neurons,":[37],"analyzes":[39],"global":[40,67],"attractors":[41,97],"based":[42],"on":[43,54,75],"parameterized":[45],"2-D":[46],"model.":[47],"On":[48],"basis":[50],"previous":[52],"results":[53],"nondegenerate":[55],"degenerate":[57],"equilibria":[58],"mathematics,":[60],"we":[61],"further":[62],"elucidate":[63],"all":[64],"possible":[65],"nontrivial":[66],"attractors.":[68],"Our":[69],"theoretical":[70,107],"result":[71],"provides":[72],"precise":[73],"descriptions":[74],"how":[76],"changes":[78],"parameters":[81],"affect":[82],"attractors'":[84],"distribution":[85],"landscape,":[87],"may":[90],"give":[91],"feasible":[93],"solution":[94],"towards":[95],"specifying":[96,99],"by":[98],"weights.":[100],"Simulations":[101],"are":[102],"presented":[103],"to":[104],"illustrate":[105],"results.":[108]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}