{"id":"https://openalex.org/W2588583345","doi":"https://doi.org/10.1162/neco_a_01069","title":"Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model","display_name":"Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model","publication_year":2018,"publication_date":"2018-03-22","ids":{"openalex":"https://openalex.org/W2588583345","doi":"https://doi.org/10.1162/neco_a_01069","mag":"2588583345","pmid":"https://pubmed.ncbi.nlm.nih.gov/29566351"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_01069","is_oa":true,"landing_page_url":"https://doi.org/10.1162/neco_a_01069","pdf_url":"https://direct.mit.edu/neco/article-pdf/30/5/1258/1036931/neco_a_01069.pdf","source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://direct.mit.edu/neco/article-pdf/30/5/1258/1036931/neco_a_01069.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040938071","display_name":"Diego Fasoli","orcid":"https://orcid.org/0000-0003-4278-6630"},"institutions":[{"id":"https://openalex.org/I4210127676","display_name":"Center for Neuroscience and Cognitive Systems","ror":"https://ror.org/045yf0774","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210127676"]},{"id":"https://openalex.org/I170486558","display_name":"Pompeu Fabra University","ror":"https://ror.org/04n0g0b29","country_code":"ES","type":"education","lineage":["https://openalex.org/I170486558"]},{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["ES","IT"],"is_corresponding":true,"raw_author_name":"Diego Fasoli","raw_affiliation_strings":["Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, 08002 Barcelona, Spain","Laboratory of Neural Computation, Center for Neuroscience and Cognitive\n Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and Center\n for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra,\n 08002 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, 08002 Barcelona, Spain","institution_ids":["https://openalex.org/I4210127676"]},{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive\n Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and Center\n for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra,\n 08002 Barcelona, Spain","institution_ids":["https://openalex.org/I4210127676","https://openalex.org/I170486558","https://openalex.org/I30771326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005500174","display_name":"Anna Cattani","orcid":"https://orcid.org/0000-0003-2317-1737"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]},{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]},{"id":"https://openalex.org/I4210127676","display_name":"Center for Neuroscience and Cognitive Systems","ror":"https://ror.org/045yf0774","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210127676"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Anna Cattani","raw_affiliation_strings":["Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and Department of Biomedical and Clinical Sciences \u201cL. Sacco,\u201d University of Milan, 20157 Milan, Italy","Laboratory of Neural Computation, Center for Neuroscience and Cognitive\n Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and\n Department of Biomedical and Clinical Sciences \"L. Sacco,\" University\n of Milan, 20157 Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and Department of Biomedical and Clinical Sciences \u201cL. Sacco,\u201d University of Milan, 20157 Milan, Italy","institution_ids":["https://openalex.org/I4210127676","https://openalex.org/I189158943","https://openalex.org/I30771326"]},{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive\n Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy, and\n Department of Biomedical and Clinical Sciences \"L. Sacco,\" University\n of Milan, 20157 Milan, Italy","institution_ids":["https://openalex.org/I4210127676","https://openalex.org/I189158943","https://openalex.org/I30771326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014847103","display_name":"Stefano Panzeri","orcid":"https://orcid.org/0000-0003-1700-8909"},"institutions":[{"id":"https://openalex.org/I4210127676","display_name":"Center for Neuroscience and Cognitive Systems","ror":"https://ror.org/045yf0774","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210127676"]},{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Stefano Panzeri","raw_affiliation_strings":["Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy","Laboratory of Neural Computation, Center for Neuroscience and Cognitive\n Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy"],"affiliations":[{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy","institution_ids":["https://openalex.org/I4210127676","https://openalex.org/I30771326"]},{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive\n Systems @UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy","institution_ids":["https://openalex.org/I4210127676","https://openalex.org/I30771326"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005500174","https://openalex.org/A5014847103","https://openalex.org/A5040938071"],"corresponding_institution_ids":["https://openalex.org/I170486558","https://openalex.org/I189158943","https://openalex.org/I30771326","https://openalex.org/I4210127676"],"apc_list":null,"apc_paid":null,"fwci":0.7407,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.67553191,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"5","first_page":"1258","last_page":"1295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998999834060669,"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":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5853009223937988},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5525965094566345},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5410500764846802},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4770469069480896},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.47544312477111816},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.44383347034454346},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4292331039905548},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42500269412994385},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37197279930114746},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2587927579879761},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23332947492599487},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2168383002281189},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12192511558532715},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11021995544433594}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5853009223937988},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5525965094566345},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5410500764846802},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4770469069480896},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.47544312477111816},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.44383347034454346},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4292331039905548},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42500269412994385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37197279930114746},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2587927579879761},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23332947492599487},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2168383002281189},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12192511558532715},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11021995544433594},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1162/neco_a_01069","is_oa":true,"landing_page_url":"https://doi.org/10.1162/neco_a_01069","pdf_url":"https://direct.mit.edu/neco/article-pdf/30/5/1258/1036931/neco_a_01069.pdf","source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:29566351","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29566351","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":"Neural computation","raw_type":null}],"best_oa_location":{"id":"doi:10.1162/neco_a_01069","is_oa":true,"landing_page_url":"https://doi.org/10.1162/neco_a_01069","pdf_url":"https://direct.mit.edu/neco/article-pdf/30/5/1258/1036931/neco_a_01069.pdf","source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320326086","display_name":"Provincia Autonoma di Trento","ror":"https://ror.org/017e99q89"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2588583345.pdf","grobid_xml":"https://content.openalex.org/works/W2588583345.grobid-xml"},"referenced_works_count":76,"referenced_works":["https://openalex.org/W94531097","https://openalex.org/W657199842","https://openalex.org/W1498550271","https://openalex.org/W1531509813","https://openalex.org/W1636623697","https://openalex.org/W1651391486","https://openalex.org/W1943406865","https://openalex.org/W1963974922","https://openalex.org/W1965880854","https://openalex.org/W1969291558","https://openalex.org/W1977549881","https://openalex.org/W1982602109","https://openalex.org/W1991871254","https://openalex.org/W2000467918","https://openalex.org/W2001226941","https://openalex.org/W2001951139","https://openalex.org/W2006529618","https://openalex.org/W2014332054","https://openalex.org/W2020174839","https://openalex.org/W2025604508","https://openalex.org/W2026273854","https://openalex.org/W2027105025","https://openalex.org/W2029654362","https://openalex.org/W2033788889","https://openalex.org/W2035482871","https://openalex.org/W2041234363","https://openalex.org/W2042192623","https://openalex.org/W2043679829","https://openalex.org/W2053100455","https://openalex.org/W2053638262","https://openalex.org/W2058828657","https://openalex.org/W2061564920","https://openalex.org/W2069519142","https://openalex.org/W2073099386","https://openalex.org/W2080277460","https://openalex.org/W2081696580","https://openalex.org/W2083517661","https://openalex.org/W2087058693","https://openalex.org/W2090375041","https://openalex.org/W2090414491","https://openalex.org/W2092632480","https://openalex.org/W2093386234","https://openalex.org/W2095921032","https://openalex.org/W2097311594","https://openalex.org/W2103934527","https://openalex.org/W2105031232","https://openalex.org/W2108103256","https://openalex.org/W2116733726","https://openalex.org/W2123042723","https://openalex.org/W2128084896","https://openalex.org/W2129207384","https://openalex.org/W2135171759","https://openalex.org/W2137101191","https://openalex.org/W2137927364","https://openalex.org/W2141880824","https://openalex.org/W2142488539","https://openalex.org/W2143553955","https://openalex.org/W2145749918","https://openalex.org/W2145979309","https://openalex.org/W2149413876","https://openalex.org/W2151910747","https://openalex.org/W2157154487","https://openalex.org/W2162717455","https://openalex.org/W2167809052","https://openalex.org/W2172513721","https://openalex.org/W2528603494","https://openalex.org/W2755354344","https://openalex.org/W3099892959","https://openalex.org/W3101772483","https://openalex.org/W3102660117","https://openalex.org/W3106063097","https://openalex.org/W4206502013","https://openalex.org/W4206651839","https://openalex.org/W4241400578","https://openalex.org/W4297810663","https://openalex.org/W4299432846"],"related_works":["https://openalex.org/W1861797342","https://openalex.org/W2950310075","https://openalex.org/W4366459492","https://openalex.org/W2952962099","https://openalex.org/W2564990357","https://openalex.org/W2771785338","https://openalex.org/W391927469","https://openalex.org/W2011180239","https://openalex.org/W1846433012","https://openalex.org/W4299649768"],"abstract_inverted_index":{"Despite":[0],"their":[1,291],"biological":[2],"plausibility,":[3],"neural":[4,40,222],"network":[5,60,157,194,226,277,285],"models":[6],"with":[7,42,77,143,186,255],"asymmetric":[8,36,205],"weights":[9],"are":[10,17,244,251],"rarely":[11],"solved":[12,266],"analytically,":[13],"and":[14,50,56,66,70,87,96,123,140,171,208,240,287],"closed-form":[15],"solutions":[16,33],"available":[18],"only":[19,267],"in":[20,25,159,224,227,279],"some":[21,26],"limiting":[22],"cases":[23],"or":[24,247],"mean-field":[27],"approximations.":[28],"We":[29,80,163,215],"found":[30,81],"exact":[31],"analytical":[32,82,296],"of":[34,39,84,92,106,136,138,155,167,176,211,221,258,283],"an":[35],"spin":[37],"model":[38],"networks":[41,114,254],"arbitrary":[43],"size":[44,286],"without":[45],"resorting":[46],"to":[47,112],"any":[48,78,256],"approximation,":[49],"we":[51,110,150,273,288],"comprehensively":[52],"studied":[53,151,290],"its":[54],"dynamical":[55],"statistical":[57],"properties.":[58],"The":[59,125],"had":[61],"discrete":[62],"time":[63],"evolution":[64],"equations":[65,262,278],"binary":[67],"firing":[68,98,108,242],"rates,":[69,109],"it":[71],"could":[72],"be":[73,264],"driven":[74],"by":[75,121,204,301],"noise":[76],"distribution.":[79],"expressions":[83],"the":[85,93,97,102,107,115,130,134,152,156,160,168,177,182,187,193,225,228,237,241,276,280,295],"conditional":[86,103],"stationary":[88,229],"joint":[89],"probability":[90,104],"distributions":[91],"membrane":[94,238],"potentials":[95,239],"rates.":[99],"By":[100],"manipulating":[101],"distribution":[105],"extend":[111],"stochastic":[113],"associating":[116],"learning":[117,127],"rule":[118,128],"previously":[119],"introduced":[120],"Personnaz":[122],"coworkers.":[124],"new":[126],"allowed":[129],"safe":[131],"storage,":[132],"under":[133],"presence":[135],"noise,":[137],"point":[139],"cyclic":[141],"attractors,":[142],"useful":[144],"implications":[145],"for":[146,253,268],"content-addressable":[147],"memories.":[148],"Furthermore,":[149],"bifurcation":[153,174],"structure":[154],"dynamics":[158,184],"zero-noise":[161],"limit.":[162],"analytically":[164,218,289],"derived":[165,275],"examples":[166],"codimension":[169,172],"1":[170],"2":[173],"diagrams":[175],"network,":[178],"which":[179],"describe":[180],"how":[181],"neuronal":[183,233],"changes":[185],"external":[188],"stimuli.":[189],"This":[190,231],"showed":[191],"that":[192],"may":[195],"undergo":[196],"transitions":[197],"among":[198],"multistable":[199],"regimes,":[200],"oscillatory":[201],"behavior":[202],"elicited":[203],"synaptic":[206],"connections,":[207],"various":[209],"forms":[210],"spontaneous":[212],"symmetry":[213],"breaking.":[214],"also":[216,274],"calculated":[217],"groupwise":[219],"correlations":[220],"activity":[223],"regime.":[230],"revealed":[232],"regimes":[234],"where,":[235],"statistically,":[236],"rates":[243],"either":[245],"synchronous":[246],"asynchronous.":[248],"Our":[249],"results":[250,297],"valid":[252],"number":[257],"neurons,":[259],"although":[260],"our":[261],"can":[263],"realistically":[265],"small":[269],"networks.":[270],"For":[271],"completeness,":[272],"thermodynamic":[281],"limit":[282],"infinite":[284],"local":[292],"bifurcations.":[293],"All":[294],"were":[298],"extensively":[299],"validated":[300],"numerical":[302],"simulations.":[303]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}