{"id":"https://openalex.org/W1981880767","doi":"https://doi.org/10.1137/090760751","title":"Convergence in Strongly Monotone Systems with an Increasing First Integral","display_name":"Convergence in Strongly Monotone Systems with an Increasing First Integral","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1981880767","doi":"https://doi.org/10.1137/090760751","mag":"1981880767"},"language":"en","primary_location":{"id":"doi:10.1137/090760751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090760751","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5034799827","display_name":"Murad Banaji","orcid":"https://orcid.org/0000-0002-4983-0377"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Murad Banaji","raw_affiliation_strings":["School of Mathematics and Physics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037354850","display_name":"David Angeli","orcid":"https://orcid.org/0000-0002-5311-4306"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]},{"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","IT"],"is_corresponding":false,"raw_author_name":"David Angeli","raw_affiliation_strings":["University of Florence, Italy","Dept. of Electrical and Electronic Engineering, Imperial College London, UK, and Dip. Sistemi e Informatica,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florence, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dept. of Electrical and Electronic Engineering, Imperial College London, UK, and Dip. Sistemi e Informatica,","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5588,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.88852718,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"42","issue":"1","first_page":"334","last_page":"353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/orthant","display_name":"Orthant","score":0.9341739416122437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8558019399642944},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7465760707855225},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7341629266738892},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6030212640762329},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5550758242607117},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.44476965069770813},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4358283579349518},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42556700110435486},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37701350450515747},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3199547529220581},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12082871794700623}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.9341739416122437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8558019399642944},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7465760707855225},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7341629266738892},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6030212640762329},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5550758242607117},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.44476965069770813},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4358283579349518},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42556700110435486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37701350450515747},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3199547529220581},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12082871794700623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/090760751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090760751","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:eprints.lancs.ac.uk:231079","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/231079/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.248.9993","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.9993","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/0906.0272v1.pdf","raw_type":"text"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:146843","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/146843/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM J Math Anal , 42  (1)   pp. 334-353.   (2010)      ","raw_type":"Article"},{"id":"pmh:oai:researchportal.port.ac.uk:publications/59fa9c9b-3443-43c0-b1e3-ca1986bb7834","is_oa":false,"landing_page_url":"https://researchportal.port.ac.uk/portal/en/publications/convergence-in-strongly-monotone-systems-with-an-increasing-first-integral(59fa9c9b-3443-43c0-b1e3-ca1986bb7834).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401774","display_name":"Portsmouth Research Portal (University of Portsmouth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63072094","host_organization_name":"University of Portsmouth","host_organization_lineage":["https://openalex.org/I63072094"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2113131027","display_name":null,"funder_award_id":"EP/D060982/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W240844920","https://openalex.org/W1500921805","https://openalex.org/W1537538358","https://openalex.org/W1851248039","https://openalex.org/W1984006289","https://openalex.org/W1987635542","https://openalex.org/W2010060766","https://openalex.org/W2012719969","https://openalex.org/W2041816179","https://openalex.org/W2049625365","https://openalex.org/W2050872434","https://openalex.org/W2059998662","https://openalex.org/W2090032951","https://openalex.org/W2104107528","https://openalex.org/W2159807606","https://openalex.org/W2166127999","https://openalex.org/W3107709063"],"related_works":["https://openalex.org/W2102386043","https://openalex.org/W1978168956","https://openalex.org/W2019002977","https://openalex.org/W3120093433","https://openalex.org/W2010120149","https://openalex.org/W4286585382","https://openalex.org/W4299336084","https://openalex.org/W2951013428","https://openalex.org/W4287900645","https://openalex.org/W2064567872"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,94],"generalize":[4],"a":[5,15,73,90],"useful":[6],"result":[7],"due":[8],"to":[9,85],"Mierczy\u0144ski":[10],"which":[11,79,88],"states":[12],"that":[13,96],"for":[14],"strictly":[16],"cooperative":[17],"system":[18],"on":[19,41,77,110],"the":[20],"positive":[21],"orthant,":[22],"with":[23,83],"increasing":[24],"first":[25,92],"integral,":[26,93],"all":[27],"bounded":[28,98],"orbits":[29],"are":[30,62],"convergent.":[31],"Moreover":[32],"there":[33,102],"can":[34,103],"be":[35,67,104],"no":[36,105],"more":[37,54,59,106],"than":[38,107],"one":[39,108],"equilibrium":[40,47,109,116],"any":[42,46,68,111],"level":[43,51,112,120],"set,":[44,113],"and":[45,58,87,114],"attracts":[48,117],"its":[49,118],"entire":[50,119],"set.":[52,121],"Here,":[53],"general":[55,60],"state":[56],"spaces":[57],"orderings":[61],"considered.":[63],"Let":[64],"$Y\\subset":[65],"K\\subset\\mathbb{R}^n$":[66],"two":[69],"proper":[70],"cones.":[71],"Given":[72],"local":[74],"semiflow":[75],"$\\phi$":[76],"Y":[78],"is":[80,127],"strongly":[81],"monotone":[82],"respect":[84],"K,":[86],"preserves":[89],"K-increasing":[91],"show":[95],"every":[97],"orbit":[99],"converges.":[100],"Again,":[101],"each":[115],"An":[122],"application":[123],"from":[124],"chemical":[125],"dynamics":[126],"provided.":[128]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}