{"id":"https://openalex.org/W2137023886","doi":"https://doi.org/10.1109/tnn.2010.2102048","title":"On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks","display_name":"On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks","publication_year":2011,"publication_date":"2011-01-07","ids":{"openalex":"https://openalex.org/W2137023886","doi":"https://doi.org/10.1109/tnn.2010.2102048","mag":"2137023886","pmid":"https://pubmed.ncbi.nlm.nih.gov/21216708"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2010.2102048","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2010.2102048","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/A5110221627","display_name":"Wenlian Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenlian Lu","raw_affiliation_strings":["Center for Computational Systems Biology and School of Mathematical Science, Fudan University, Shanghai 200433, China. wenlian@fudan.edu.cn","Center for Comput. Syst. Biol., Fudan Univ., Shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Systems Biology and School of Mathematical Science, Fudan University, Shanghai 200433, China. wenlian@fudan.edu.cn","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Center for Comput. Syst. Biol., Fudan Univ., Shanghai, China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100755690","display_name":"Lili Wang","orcid":"https://orcid.org/0000-0002-3531-3918"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lili Wang","raw_affiliation_strings":["Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, China","Dept. of Appl. Math., Shanghai Univ. of Finance & Econ., Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, China","institution_ids":["https://openalex.org/I181679659"]},{"raw_affiliation_string":"Dept. of Appl. Math., Shanghai Univ. of Finance & Econ., Shanghai, China","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062509066","display_name":"Tianping Chen","orcid":"https://orcid.org/0000-0001-6117-6673"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianping Chen","raw_affiliation_strings":["Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, China","Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.7767,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.97991198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"3","first_page":"381","last_page":"394"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attraction","display_name":"Attraction","score":0.6639792323112488},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6570346355438232},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6412461996078491},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6087135076522827},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5567288398742676},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5444688200950623},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.49330082535743713},{"id":"https://openalex.org/keywords/cellular-neural-network","display_name":"Cellular neural network","score":0.4542374014854431},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44381511211395264},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.43076273798942566},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4279506504535675},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4167824983596802},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3849658966064453},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3561529219150543},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33434003591537476},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1971909999847412},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19445759057998657},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10551261901855469}],"concepts":[{"id":"https://openalex.org/C2778364177","wikidata":"https://www.wikidata.org/wiki/Q2247133","display_name":"Attraction","level":2,"score":0.6639792323112488},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6570346355438232},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6412461996078491},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6087135076522827},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5567288398742676},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5444688200950623},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.49330082535743713},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.4542374014854431},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44381511211395264},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.43076273798942566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4279506504535675},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4167824983596802},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3849658966064453},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3561529219150543},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33434003591537476},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1971909999847412},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19445759057998657},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10551261901855469},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","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":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","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":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnn.2010.2102048","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2010.2102048","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:21216708","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21216708","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}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1589876408","https://openalex.org/W1966864455","https://openalex.org/W1974672421","https://openalex.org/W1989191559","https://openalex.org/W2014116791","https://openalex.org/W2016020597","https://openalex.org/W2025294622","https://openalex.org/W2026174587","https://openalex.org/W2038088369","https://openalex.org/W2049929575","https://openalex.org/W2056717940","https://openalex.org/W2057553352","https://openalex.org/W2060813275","https://openalex.org/W2065134213","https://openalex.org/W2071410910","https://openalex.org/W2081257826","https://openalex.org/W2085982859","https://openalex.org/W2094128026","https://openalex.org/W2100471656","https://openalex.org/W2104130992","https://openalex.org/W2107025852","https://openalex.org/W2107704411","https://openalex.org/W2112056482","https://openalex.org/W2113173391","https://openalex.org/W2121752938","https://openalex.org/W2129060839","https://openalex.org/W2133419206","https://openalex.org/W2133838859","https://openalex.org/W2145729548","https://openalex.org/W2147514436","https://openalex.org/W2156564598","https://openalex.org/W2160121923","https://openalex.org/W2166726747","https://openalex.org/W2169273485","https://openalex.org/W2170767382","https://openalex.org/W2170790343","https://openalex.org/W2171434780","https://openalex.org/W2171925415","https://openalex.org/W2610857016","https://openalex.org/W2742470390","https://openalex.org/W4234336054","https://openalex.org/W4241290540","https://openalex.org/W6679768172"],"related_works":["https://openalex.org/W1918046727","https://openalex.org/W2063711684","https://openalex.org/W1504744809","https://openalex.org/W2095639497","https://openalex.org/W2076653911","https://openalex.org/W2152189682","https://openalex.org/W2106935906","https://openalex.org/W2164689297","https://openalex.org/W2010475740","https://openalex.org/W2064956727"],"abstract_inverted_index":{"In":[0],"this":[1,58],"paper,":[2],"we":[3,73],"study":[4],"the":[5,22,25,29,41,44,61,65,75,84,89,93,100,113,118,127],"distribution":[6],"of":[7,10,14,24,28,32,40,43,47,50,57,78,82,88,92,103,107,116],"attraction":[8,76],"basins":[9,27,102],"multiple":[11],"equilibrium":[12,81],"points":[13],"cellular":[15],"neural":[16],"networks":[17],"(CNNs).":[18],"Under":[19],"several":[20],"conditions,":[21],"boundaries":[23],"attracting":[26,101],"stable":[30,35,45,69,80,90,119,129,133],"equilibria":[31,49,95,115,134],"a":[33,104],"completely":[34,128],"CNN":[36],"system":[37],"are":[38],"composed":[39,87],"closures":[42],"manifolds":[46,91],"unstable":[48,71,94,114],"(n":[51,122],"-":[52,123],"1)":[53,124],"dimensions.":[54],"As":[55],"demonstrations":[56],"idea,":[59],"under":[60],"conditions":[62],"proposed":[63],"in":[64],"literature":[66],"which":[67,83,117],"depicts":[68],"and":[70,126],"equilibria,":[72],"identify":[74],"basin":[77],"each":[79],"boundary":[85],"is":[86,121],"precisely.":[96],"We":[97],"also":[98],"investigate":[99],"simple":[105],"class":[106],"symmetric":[108],"1-D":[109],"CNNs":[110,131],"via":[111],"identifying":[112],"manifold":[120],"dimensional":[125],"asymmetric":[130],"with":[132],"less":[135],"than":[136],"2(n).":[137]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}