{"id":"https://openalex.org/W4413812186","doi":"https://doi.org/10.1142/s0218127425501639","title":"Detecting Transitions from Steady States to Chaos with Gamma Distribution","display_name":"Detecting Transitions from Steady States to Chaos with Gamma Distribution","publication_year":2025,"publication_date":"2025-08-29","ids":{"openalex":"https://openalex.org/W4413812186","doi":"https://doi.org/10.1142/s0218127425501639"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425501639","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501639","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"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":"International Journal of Bifurcation and Chaos","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/A5091211890","display_name":"Haiyan Wang","orcid":"https://orcid.org/0000-0002-5204-967X"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Haiyan Wang","raw_affiliation_strings":["School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, USA"],"raw_orcid":"https://orcid.org/0000-0002-5204-967X","affiliations":[{"raw_affiliation_string":"School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031612883","display_name":"Ying Wang","orcid":"https://orcid.org/0000-0003-3188-2563"},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ying Wang","raw_affiliation_strings":["Department of Mathematics, University of Oklahoma, Norman, OK 73019-3103, USA"],"raw_orcid":"https://orcid.org/0000-0003-3188-2563","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oklahoma, Norman, OK 73019-3103, USA","institution_ids":["https://openalex.org/I8692664"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3768,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.91438467,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"35","issue":"13","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.7918000221252441,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.7918000221252441,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.709322452545166},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6006596684455872},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5544167160987854},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.4970231354236603},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.49398523569107056},{"id":"https://openalex.org/keywords/gamma-distribution","display_name":"Gamma distribution","score":0.4525071084499359},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.41195639967918396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3547401428222656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2670893967151642},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2576698660850525},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15411311388015747},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11592921614646912}],"concepts":[{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.709322452545166},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6006596684455872},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5544167160987854},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.4970231354236603},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.49398523569107056},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.4525071084499359},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.41195639967918396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3547401428222656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2670893967151642},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2576698660850525},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15411311388015747},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11592921614646912},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127425501639","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501639","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"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":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1537236879","https://openalex.org/W2038954595","https://openalex.org/W2056942998","https://openalex.org/W2073554231","https://openalex.org/W2078303508","https://openalex.org/W2099593264","https://openalex.org/W2100891518","https://openalex.org/W2102892532","https://openalex.org/W2152254020","https://openalex.org/W2161177537","https://openalex.org/W2331057793","https://openalex.org/W2489691424","https://openalex.org/W2570230195","https://openalex.org/W2998043344","https://openalex.org/W3168387901","https://openalex.org/W4256081943","https://openalex.org/W4298084067","https://openalex.org/W4392452014","https://openalex.org/W4394760427","https://openalex.org/W4399723707","https://openalex.org/W4407317637"],"related_works":["https://openalex.org/W2320196587","https://openalex.org/W4400519012","https://openalex.org/W4243901518","https://openalex.org/W4383267773","https://openalex.org/W3110439525","https://openalex.org/W4251075027","https://openalex.org/W2004708907","https://openalex.org/W2393451533","https://openalex.org/W2356296294","https://openalex.org/W2156996747"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"a":[5,92,95,104,133],"novel":[6],"method":[7],"to":[8,14,32,52,73,97],"identify":[9],"transitions":[10],"from":[11,94],"steady":[12],"states":[13,76],"chaos":[15,138],"in":[16,127,139],"stochastic":[17,49,61],"models,":[18],"specifically":[19],"focusing":[20],"on":[21],"the":[22,29,34,43,48,60,68,86,99,107,111,124],"logistic":[23,87],"and":[24,80],"Ricker":[25,100],"equations":[26,50,62],"by":[27,39,78],"leveraging":[28],"gamma":[30,112],"distribution":[31,113],"describe":[33],"underlying":[35],"population.":[36],"We":[37],"begin":[38],"showing":[40],"that":[41,59],"when":[42,106],"variance":[44],"is":[45,114],"sufficiently":[46],"small,":[47],"converge":[51],"their":[53],"deterministic":[54],"counterparts.":[55],"Our":[56],"analysis":[57],"reveals":[58],"exhibit":[63],"two":[64],"distinct":[65],"branches":[66],"of":[67,110,123],"intrinsic":[69],"growth":[70,82],"rate,":[71],"corresponding":[72],"alternative":[74],"stable":[75],"characterized":[77],"higher":[79],"lower":[81],"rates.":[83],"Notably,":[84],"while":[85],"model":[88,101],"does":[89],"not":[90,118],"show":[91],"transition":[93,105],"steady-state":[96],"chaos,":[98],"undergoes":[102],"such":[103],"shape":[108],"parameter":[109],"small.":[115],"These":[116],"findings":[117],"only":[119],"enhance":[120],"our":[121],"understanding":[122],"dynamic":[125],"behavior":[126],"biological":[128],"populations":[129],"but":[130],"also":[131],"provide":[132],"robust":[134],"framework":[135],"for":[136],"detecting":[137],"complex":[140],"systems.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}