{"id":"https://openalex.org/W2122902581","doi":"https://doi.org/10.1142/s0219525911002895","title":"ON THE RELATION BETWEEN ORGANIZATIONS AND LIMIT SETS IN CHEMICAL REACTION SYSTEMS","display_name":"ON THE RELATION BETWEEN ORGANIZATIONS AND LIMIT SETS IN CHEMICAL REACTION SYSTEMS","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2122902581","doi":"https://doi.org/10.1142/s0219525911002895","mag":"2122902581"},"language":"en","primary_location":{"id":"doi:10.1142/s0219525911002895","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525911002895","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Complex Systems","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/A5084087535","display_name":"Stephan Peter","orcid":"https://orcid.org/0000-0003-1540-190X"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"STEPHAN PETER","raw_affiliation_strings":["Bio Systems Analysis Group, Jena Centre for Bioinformatics (JCB) and Department for Mathematics and Computer Sciences, Friedrich Schiller University of Jena, D-07743 Jena, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bio Systems Analysis Group, Jena Centre for Bioinformatics (JCB) and Department for Mathematics and Computer Sciences, Friedrich Schiller University of Jena, D-07743 Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018987403","display_name":"Peter Dittrich","orcid":"https://orcid.org/0000-0002-2541-6745"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"PETER DITTRICH","raw_affiliation_strings":["Bio Systems Analysis Group, Jena Centre for Bioinformatics (JCB) and Department for Mathematics and Computer Sciences, Friedrich Schiller University of Jena, D-07743 Jena, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bio Systems Analysis Group, Jena Centre for Bioinformatics (JCB) and Department for Mathematics and Computer Sciences, Friedrich Schiller University of Jena, D-07743 Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I76198965"],"apc_list":null,"apc_paid":null,"fwci":0.7869,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.71484719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"01","first_page":"77","last_page":"96"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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":0.993399977684021,"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/T10932","display_name":"Microbial Metabolic Engineering and Bioproduction","score":0.9857000112533569,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.741649866104126},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.671273410320282},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6430196166038513},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.615630030632019},{"id":"https://openalex.org/keywords/limit-set","display_name":"Limit set","score":0.5220370292663574},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5059930682182312},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.49313730001449585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4600323438644409},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.42729637026786804},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4254131317138672},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3811691999435425},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37758171558380127},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3281601071357727},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2423073649406433},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21963092684745789},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08501654863357544}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.741649866104126},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.671273410320282},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6430196166038513},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.615630030632019},{"id":"https://openalex.org/C51337361","wikidata":"https://www.wikidata.org/wiki/Q1825444","display_name":"Limit set","level":3,"score":0.5220370292663574},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5059930682182312},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.49313730001449585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4600323438644409},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.42729637026786804},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4254131317138672},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3811691999435425},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37758171558380127},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3281601071357727},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2423073649406433},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21963092684745789},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08501654863357544},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219525911002895","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525911002895","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Complex Systems","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:acsxxx:v:14:y:2011:i:01:n:s0219525911002895","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219525911002895","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:RePEc:wsi:acsxxx:v:14:y:2011:i:01:p:77-96","is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0219525911002895","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.7300000190734863}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W130878554","https://openalex.org/W619425183","https://openalex.org/W1492040047","https://openalex.org/W1841330889","https://openalex.org/W1965721509","https://openalex.org/W1994656497","https://openalex.org/W1999104080","https://openalex.org/W2007020702","https://openalex.org/W2011214280","https://openalex.org/W2012498147","https://openalex.org/W2021767817","https://openalex.org/W2026541477","https://openalex.org/W2032150785","https://openalex.org/W2066718612","https://openalex.org/W2084126943","https://openalex.org/W2091734849","https://openalex.org/W2099039198","https://openalex.org/W2113372190","https://openalex.org/W2164003937","https://openalex.org/W2289587704","https://openalex.org/W2402709285","https://openalex.org/W3102310679","https://openalex.org/W4237997615"],"related_works":["https://openalex.org/W2048010006","https://openalex.org/W2963607904","https://openalex.org/W2202870442","https://openalex.org/W2945666329","https://openalex.org/W2363533283","https://openalex.org/W2081648287","https://openalex.org/W3186780583","https://openalex.org/W4323927134","https://openalex.org/W2050682984","https://openalex.org/W2617651062"],"abstract_inverted_index":{"Chemical":[0],"organization":[1],"theory":[2],"has":[3],"been":[4],"suggested":[5],"as":[6],"a":[7,32,46,67,80,91,140,191],"new":[8],"approach":[9],"to":[10,45,196],"analyze":[11],"complex":[12],"reaction":[13,49,197],"networks.":[14],"Concerning":[15],"the":[16,20,55,59,88,96,102,107,153,168],"long-term":[17,108],"behavior":[18,57],"of":[19,37,48,58,61,104,128,170,178],"network":[21],"dynamics":[22],"we":[23,30,78],"will":[24],"study":[25],"its":[26],"foundations":[27],"mathematically.":[28],"Therefore":[29],"consider":[31,79],"chemical":[33,69,141],"reactor":[34,89],"containing":[35],"molecules":[36],"different":[38],"species":[39,63,84,105,171,202],"reacting":[40],"with":[41,172],"each":[42,62],"other":[43],"according":[44,195],"set":[47,98,169],"rules.":[50],"We":[51,94,110],"further":[52],"assume":[53],"that":[54,112,119,146,149,166,204],"dynamical":[56],"concentration":[60,76],"is":[64,130,134,182],"given":[65],"by":[66],"continuous":[68],"ordinary":[70,142],"differential":[71,143],"equation.":[72],"Abstracting":[73],"from":[74],"dedicated":[75],"values":[77],"discrete":[81],"problem:":[82],"Which":[83],"can":[85,200],"appear":[86],"in":[87,175,186,190],"after":[90],"long":[92],"time?":[93],"define":[95],"limit":[97,123],"abstraction,":[99],"which":[100],"contains":[101],"subsets":[103,115],"characterizing":[106],"behavior.":[109],"prove":[111],"all":[113,121],"these":[114],"are":[116,205],"closed":[117,206],"and":[118,132,207],"for":[120,139],"bounded":[122],"sets,":[124],"at":[125],"least":[126],"one":[127,164,199],"them":[129],"self-maintaining":[131],"thus":[133,209],"an":[135,180,183],"organization.":[136,184],"This":[137,185],"implies":[138],"equation":[144],"systems":[145],"any":[147,159,176],"attractor":[148,181],"does":[150],"not":[151],"touch":[152],"state":[154,177],"space":[155],"boundaries":[156],"(in":[157],"particular,":[158],"periodic":[160],"attractor)":[161],"lies":[162],"within":[163],"organization,":[165],"is,":[167],"positive":[173],"concentrations":[174],"such":[179],"turn":[187],"explains":[188],"why":[189],"deterministic":[192],"system":[193],"evolving":[194],"rules":[198],"observe":[201],"sets":[203],"self-maintaining,":[208],"organizations.":[210]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}