{"id":"https://openalex.org/W2062448723","doi":"https://doi.org/10.1137/s0363012900361178","title":"Extension of the Perron--Frobenius Theorem to Homogeneous Systems","display_name":"Extension of the Perron--Frobenius Theorem to Homogeneous Systems","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2062448723","doi":"https://doi.org/10.1137/s0363012900361178","mag":"2062448723"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012900361178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900361178","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5054699708","display_name":"Dirk Aeyels","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dirk Aeyels","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109213702","display_name":"Patrick De Leenheer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patrick De Leenheer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.033,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.80607548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"41","issue":"2","first_page":"563","last_page":"582"},"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":0.9975000023841858,"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":0.9975000023841858,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9923999905586243,"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":0.9850174784660339},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9084957838058472},{"id":"https://openalex.org/keywords/positive-systems","display_name":"Positive systems","score":0.6448705196380615},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6314005255699158},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5886577367782593},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.578335165977478},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5265840888023376},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4839377999305725},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4572041630744934},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.43900126218795776},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4265121817588806},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.38248443603515625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.375213623046875},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.29651379585266113},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1839050054550171},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09238171577453613}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.9850174784660339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9084957838058472},{"id":"https://openalex.org/C2778299942","wikidata":"https://www.wikidata.org/wiki/Q7233296","display_name":"Positive systems","level":3,"score":0.6448705196380615},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6314005255699158},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5886577367782593},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.578335165977478},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5265840888023376},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4839377999305725},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4572041630744934},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.43900126218795776},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4265121817588806},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.38248443603515625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.375213623046875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29651379585266113},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1839050054550171},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09238171577453613},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0363012900361178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900361178","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:archive.ugent.be:161000","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-161000","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0363-0129","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W624020015","https://openalex.org/W1500921805","https://openalex.org/W1527177198","https://openalex.org/W1979392834","https://openalex.org/W2054971406","https://openalex.org/W2085728653","https://openalex.org/W2135152519","https://openalex.org/W2151596144","https://openalex.org/W2166127999","https://openalex.org/W2489426763","https://openalex.org/W3038830718","https://openalex.org/W3141151088","https://openalex.org/W4211137119","https://openalex.org/W4254127125"],"related_works":["https://openalex.org/W2220253973","https://openalex.org/W1905581482","https://openalex.org/W2000898041","https://openalex.org/W2991666192","https://openalex.org/W2131032422","https://openalex.org/W3186957793","https://openalex.org/W2186188480","https://openalex.org/W2968514504","https://openalex.org/W4300784672","https://openalex.org/W3203676140"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,103],"a":[4,14,131],"particular":[5,45],"class":[6,46],"of":[7,13,63,66,78,99,115,134,138],"positive":[8,15,18,23,139],"systems.":[9,72,141],"The":[10,83,112],"state":[11],"components":[12],"system":[16],"are":[17,27,81],"or":[19,37],"zero":[20,101],"for":[21,43,76],"all":[22],"times.":[24],"These":[25],"systems":[26,68],"often":[28],"encountered":[29],"in":[30,54,108],"applied":[31],"areas":[32],"such":[33],"as":[34],"chemical":[35],"engineering":[36],"biology.":[38],"It":[39],"is":[40,118],"shown":[41],"that":[42,87],"this":[44,79],"the":[47,61,88,96,100,109,116,126,135],"first":[48,110],"orthant":[49],"contains":[50],"an":[51,64,92],"invariant":[52,58,93],"ray":[53,59,80,94],"its":[55],"interior.":[56],"An":[57],"generalizes":[60],"concept":[62],"eigenvector":[65],"linear":[67,140],"to":[69,105,125],"nonlinear":[70],"homogeneous":[71],"Then":[73],"sufficient":[74],"conditions":[75,107],"uniqueness":[77],"given.":[82],"main":[84],"result":[85],"states":[86],"vector":[89],"field":[90],"on":[91],"determines":[95],"stability":[97],"properties":[98],"solution":[102],"respect":[104],"initial":[106],"orthant.":[111],"asymptotic":[113],"behavior":[114,137],"solutions":[117],"examined.":[119],"Finally,":[120],"we":[121],"compare":[122],"our":[123],"results":[124],"Perron--Frobenius":[127],"theorem,":[128],"which":[129],"gives":[130],"detailed":[132],"picture":[133],"dynamical":[136]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
