{"id":"https://openalex.org/W2143741733","doi":"https://doi.org/10.1137/130928170","title":"A Geometric Approach to the Global Attractor Conjecture","display_name":"A Geometric Approach to the Global Attractor Conjecture","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2143741733","doi":"https://doi.org/10.1137/130928170","mag":"2143741733"},"language":"en","primary_location":{"id":"doi:10.1137/130928170","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130928170","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1305.5303","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014099796","display_name":"Manoj Gopalkrishnan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Manoj Gopalkrishnan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016020455","display_name":"Ezra Miller","orcid":"https://orcid.org/0000-0003-0858-586X"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ezra Miller","raw_affiliation_strings":["Duke University"],"affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042332739","display_name":"Anne Shiu","orcid":"https://orcid.org/0000-0002-5358-3049"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anne Shiu","raw_affiliation_strings":["University-of Chicago"],"affiliations":[{"raw_affiliation_string":"University-of Chicago","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014099796"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.7738,"has_fulltext":false,"cited_by_count":109,"citation_normalized_percentile":{"value":0.98271703,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"13","issue":"2","first_page":"758","last_page":"797"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/mathematics","display_name":"Mathematics","score":0.703662633895874},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5611598491668701},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5437345504760742},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5233240127563477},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.4797040820121765},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4604436159133911},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4291646480560303},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23565298318862915},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19063040614128113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1616429090499878}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.703662633895874},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5611598491668701},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5437345504760742},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5233240127563477},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4797040820121765},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4604436159133911},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4291646480560303},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23565298318862915},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19063040614128113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1616429090499878},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130928170","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130928170","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1305.5303","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1305.5303","pdf_url":"https://arxiv.org/pdf/1305.5303","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.743.5016","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.743.5016","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1305.5303.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1305.5303","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1305.5303","pdf_url":"https://arxiv.org/pdf/1305.5303","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W130878554","https://openalex.org/W432429310","https://openalex.org/W596494530","https://openalex.org/W642365271","https://openalex.org/W1466650115","https://openalex.org/W1482637285","https://openalex.org/W1491267144","https://openalex.org/W1495984520","https://openalex.org/W1584154100","https://openalex.org/W1597196612","https://openalex.org/W1607684789","https://openalex.org/W1666773027","https://openalex.org/W1963626066","https://openalex.org/W1976991265","https://openalex.org/W1977738976","https://openalex.org/W1988741929","https://openalex.org/W1991482214","https://openalex.org/W1995713768","https://openalex.org/W1997682553","https://openalex.org/W1997710477","https://openalex.org/W2019582172","https://openalex.org/W2025065282","https://openalex.org/W2025569385","https://openalex.org/W2027343907","https://openalex.org/W2028773706","https://openalex.org/W2032681364","https://openalex.org/W2033062613","https://openalex.org/W2034787898","https://openalex.org/W2036546758","https://openalex.org/W2049611659","https://openalex.org/W2071705258","https://openalex.org/W2072426122","https://openalex.org/W2078057071","https://openalex.org/W2078910282","https://openalex.org/W2080689202","https://openalex.org/W2094781369","https://openalex.org/W2102450454","https://openalex.org/W2115263319","https://openalex.org/W2116285521","https://openalex.org/W2116591110","https://openalex.org/W2119387196","https://openalex.org/W2135983136","https://openalex.org/W2145818164","https://openalex.org/W2158631240","https://openalex.org/W2159807606","https://openalex.org/W2164198012","https://openalex.org/W2164337586","https://openalex.org/W2168267705","https://openalex.org/W2950860266","https://openalex.org/W2963012918","https://openalex.org/W2963183467","https://openalex.org/W2963237893","https://openalex.org/W3098052815","https://openalex.org/W3100479371","https://openalex.org/W4245338289","https://openalex.org/W4302617909"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W1494268238","https://openalex.org/W154868527","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W1516574938","https://openalex.org/W2625725254","https://openalex.org/W2563912921"],"abstract_inverted_index":{"This":[0,54],"paper":[1],"introduces":[2],"the":[3,12,26,46,64],"class":[4,71],"of":[5,11,99,102,111,117,125,133],"strongly":[6,36],"endotactic":[7,13],"networks,":[8],"a":[9,56,82,92,105,112,128],"subclass":[10],"networks":[14],"introduced":[15],"by":[16,51,59,139],"Craciun,":[17],"Nazarov,":[18],"and":[19,122],"Pantea.":[20],"The":[21,74,88],"main":[22],"result":[23,58,130],"states":[24],"that":[25,34,84,108],"global":[27],"attractor":[28],"conjecture":[29],"holds":[30],"for":[31,61],"complex-balanced":[32],"systems":[33,62,118],"are":[35,77],"endotactic:":[37],"every":[38],"trajectory":[39],"with":[40,119,136],"positive":[41,48],"initial":[42],"condition":[43],"converges":[44],"to":[45],"unique":[47],"equilibrium":[49],"allowed":[50],"conservation":[52],"laws.":[53],"extends":[55],"recent":[57],"Anderson":[60],"where":[63],"reaction":[65,95,103],"diagram":[66],"has":[67],"only":[68],"one":[69],"linkage":[70],"(connected":[72],"component).":[73],"results":[75],"here":[76],"proved":[78],"using":[79],"differential":[80],"inclusions,":[81],"setting":[83],"includes":[85],"power-law":[86],"systems.":[87],"key":[89],"ideas":[90],"include":[91],"perspective":[93],"on":[94],"kinetics":[96],"in":[97,115],"terms":[98,116],"combinatorial":[100],"geometry":[101],"diagrams,":[104],"projection":[106],"argument":[107],"enables":[109],"analysis":[110],"given":[113],"system":[114],"lower":[120],"dimension,":[121],"an":[123],"extension":[124],"Birch's":[126],"theorem,":[127],"well-known":[129],"about":[131],"intersections":[132],"affine":[134],"subspaces":[135],"manifolds":[137],"parameterized":[138],"monomials.":[140]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}