{"id":"https://openalex.org/W1991482214","doi":"https://doi.org/10.1137/100812355","title":"Persistence and Permanence of Mass-Action and Power-Law Dynamical Systems","display_name":"Persistence and Permanence of Mass-Action and Power-Law Dynamical Systems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1991482214","doi":"https://doi.org/10.1137/100812355","mag":"1991482214"},"language":"en","primary_location":{"id":"doi:10.1137/100812355","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100812355","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 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/A5005486749","display_name":"Gheorghe Cr\u0103ciun","orcid":"https://orcid.org/0000-0003-1344-3890"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gheorghe Craciun","raw_affiliation_strings":["Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067919151","display_name":"F\u00ebdor Nazarov","orcid":"https://orcid.org/0000-0003-2892-3336"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fedor Nazarov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074239228","display_name":"Casian Pantea","orcid":"https://orcid.org/0000-0003-1921-4757"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Casian Pantea","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison","Department of Electrical Engineering, Imperial College London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Electrical Engineering, Imperial College London","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9922,"has_fulltext":false,"cited_by_count":129,"citation_normalized_percentile":{"value":0.91354125,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"73","issue":"1","first_page":"305","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9990000128746033,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.994700014591217,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9810000061988831,"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/orthant","display_name":"Orthant","score":0.8303351402282715},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6712695956230164},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6062610149383545},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5633484125137329},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.5261737108230591},{"id":"https://openalex.org/keywords/mass-action-law","display_name":"Mass action law","score":0.5150665640830994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5060777068138123},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.4854338765144348},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.46759551763534546},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4664093255996704},{"id":"https://openalex.org/keywords/living-systems","display_name":"Living systems","score":0.46404263377189636},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4520731270313263},{"id":"https://openalex.org/keywords/law-of-mass-action","display_name":"Law of mass action","score":0.42463332414627075},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.4215269684791565},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3475717306137085},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2606485188007355},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2338787317276001},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22862321138381958},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20296630263328552},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08494746685028076}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.8303351402282715},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6712695956230164},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6062610149383545},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5633484125137329},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5261737108230591},{"id":"https://openalex.org/C36543247","wikidata":"https://www.wikidata.org/wiki/Q17103208","display_name":"Mass action law","level":2,"score":0.5150665640830994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5060777068138123},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.4854338765144348},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.46759551763534546},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4664093255996704},{"id":"https://openalex.org/C2776184637","wikidata":"https://www.wikidata.org/wiki/Q6506039","display_name":"Living systems","level":2,"score":0.46404263377189636},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4520731270313263},{"id":"https://openalex.org/C67425144","wikidata":"https://www.wikidata.org/wiki/Q899494","display_name":"Law of mass action","level":2,"score":0.42463332414627075},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.4215269684791565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3475717306137085},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2606485188007355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2338787317276001},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22862321138381958},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20296630263328552},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08494746685028076},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100812355","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100812355","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2260292812","display_name":null,"funder_award_id":"R01GM086881","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"}],"funders":[{"id":"https://openalex.org/F4320309434","display_name":"University of Wisconsin-Madison","ror":"https://ror.org/01y2jtd41"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W130878554","https://openalex.org/W1502529406","https://openalex.org/W1963626066","https://openalex.org/W1980802320","https://openalex.org/W1988741929","https://openalex.org/W2027343907","https://openalex.org/W2036546758","https://openalex.org/W2053145248","https://openalex.org/W2065007796","https://openalex.org/W2078057071","https://openalex.org/W2094781369","https://openalex.org/W2116591110","https://openalex.org/W2164198012","https://openalex.org/W2169275901","https://openalex.org/W2171505650"],"related_works":["https://openalex.org/W2167267464","https://openalex.org/W2120138261","https://openalex.org/W2021967649","https://openalex.org/W2069339601","https://openalex.org/W167386789","https://openalex.org/W2339519537","https://openalex.org/W2014171690","https://openalex.org/W2466018925","https://openalex.org/W1990242716","https://openalex.org/W4362635100"],"abstract_inverted_index":{"Persistence":[0],"and":[1,16,43,45,70,122],"permanence":[2],"are":[3,37,46,67],"properties":[4],"of":[5,13,26,75,87,112],"dynamical":[6,125],"systems":[7,31,61,121],"that":[8,58,83],"describe":[9,50],"the":[10,14,24,27,51,76,100,110,137],"long-term":[11],"behavior":[12],"solutions":[15,22],"in":[17,40,53,105],"particular":[18],"specify":[19],"whether":[20],"positive":[21,28],"approach":[23],"boundary":[25],"orthant.":[29],"Mass-action":[30],"(or":[32],"more":[33],"generally":[34],"power-law":[35,120],"systems)":[36],"very":[38],"common":[39],"chemistry,":[41],"biology,":[42],"engineering":[44],"often":[47],"used":[48],"to":[49,95,119,135],"dynamics":[52],"interaction":[54],"networks.":[55],"We":[56],"prove":[57,82,136],"two-species":[59],"mass-action":[60],"derived":[62],"from":[63],"weakly":[64],"reversible":[65],"networks":[66],"both":[68],"persistent":[69],"permanent,":[71],"for":[72,109,141],"any":[73],"values":[74],"reaction":[77,101],"rate":[78,102],"parameters.":[79],"Moreover,":[80],"we":[81],"a":[84],"larger":[85],"class":[86],"networks,":[88,91],"called":[89],"endotactic":[90],"also":[92,117],"give":[93],"rise":[94],"permanent":[96],"systems,":[97],"even":[98],"if":[99],"parameters":[103],"vary":[104],"time":[106],"(to":[107],"allow":[108,133],"influence":[111],"external":[113],"signals).":[114],"These":[115],"results":[116,132],"apply":[118],"other":[123],"nonlinear":[124],"systems.":[126,143],"In":[127],"addition,":[128],"ideas":[129],"behind":[130],"these":[131],"us":[134],"global":[138],"attractor":[139],"conjecture":[140],"three-species":[142]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}