{"id":"https://openalex.org/W2574149017","doi":"https://doi.org/10.1142/s0218127416502394","title":"Qualitative Analysis of Critical Transitions in Complex Disease Propagation from a Dynamical Systems Perspective","display_name":"Qualitative Analysis of Critical Transitions in Complex Disease Propagation from a Dynamical Systems Perspective","publication_year":2016,"publication_date":"2016-12-30","ids":{"openalex":"https://openalex.org/W2574149017","doi":"https://doi.org/10.1142/s0218127416502394","mag":"2574149017"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416502394","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416502394","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/A5005042549","display_name":"Gang Wang","orcid":"https://orcid.org/0000-0003-0227-4358"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gang Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009409122","display_name":"Xiufen Zou","orcid":"https://orcid.org/0000-0001-5294-0764"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiufen Zou","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005042549"],"corresponding_institution_ids":["https://openalex.org/I37461747"],"apc_list":null,"apc_paid":null,"fwci":0.4552,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71467282,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"26","issue":"14","first_page":"1650239","last_page":"1650239"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/predictability","display_name":"Predictability","score":0.7157427072525024},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.681069016456604},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.635971188545227},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6218284368515015},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5987237691879272},{"id":"https://openalex.org/keywords/catastrophe-theory","display_name":"Catastrophe theory","score":0.5518919229507446},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.551776111125946},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.5430788993835449},{"id":"https://openalex.org/keywords/tipping-point","display_name":"Tipping point (physics)","score":0.46519482135772705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46113502979278564},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4508490562438965},{"id":"https://openalex.org/keywords/transition","display_name":"Transition (genetics)","score":0.4213762879371643},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4011598527431488},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.29641932249069214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2816459834575653},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2468814253807068},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23828473687171936},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0875234305858612},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07435974478721619},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.07259702682495117}],"concepts":[{"id":"https://openalex.org/C197640229","wikidata":"https://www.wikidata.org/wiki/Q2534066","display_name":"Predictability","level":2,"score":0.7157427072525024},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.681069016456604},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.635971188545227},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6218284368515015},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5987237691879272},{"id":"https://openalex.org/C33474566","wikidata":"https://www.wikidata.org/wiki/Q1345659","display_name":"Catastrophe theory","level":2,"score":0.5518919229507446},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.551776111125946},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.5430788993835449},{"id":"https://openalex.org/C114725131","wikidata":"https://www.wikidata.org/wiki/Q190837","display_name":"Tipping point (physics)","level":2,"score":0.46519482135772705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46113502979278564},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4508490562438965},{"id":"https://openalex.org/C194232998","wikidata":"https://www.wikidata.org/wiki/Q1606712","display_name":"Transition (genetics)","level":3,"score":0.4213762879371643},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4011598527431488},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29641932249069214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2816459834575653},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2468814253807068},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23828473687171936},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0875234305858612},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07435974478721619},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07259702682495117},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416502394","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416502394","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335577","display_name":"Major Research Plan","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1596149888","https://openalex.org/W1596321532","https://openalex.org/W1890372190","https://openalex.org/W1923514381","https://openalex.org/W1965705440","https://openalex.org/W1966512215","https://openalex.org/W1970283086","https://openalex.org/W1973279971","https://openalex.org/W1983577042","https://openalex.org/W1994224908","https://openalex.org/W2001069185","https://openalex.org/W2011866841","https://openalex.org/W2012636132","https://openalex.org/W2015576391","https://openalex.org/W2026474050","https://openalex.org/W2029018130","https://openalex.org/W2029030701","https://openalex.org/W2035255090","https://openalex.org/W2040565342","https://openalex.org/W2049168941","https://openalex.org/W2050335144","https://openalex.org/W2052287076","https://openalex.org/W2066648930","https://openalex.org/W2073141004","https://openalex.org/W2076508626","https://openalex.org/W2078582567","https://openalex.org/W2100106837","https://openalex.org/W2103948957","https://openalex.org/W2105379381","https://openalex.org/W2116199452","https://openalex.org/W2134427620","https://openalex.org/W2151958354","https://openalex.org/W2158678754","https://openalex.org/W2159806788","https://openalex.org/W2167031279","https://openalex.org/W2168047828","https://openalex.org/W2168773352","https://openalex.org/W2171549107","https://openalex.org/W2171653202","https://openalex.org/W2179664915","https://openalex.org/W2182274314","https://openalex.org/W2605543710","https://openalex.org/W2728974037","https://openalex.org/W3105221923"],"related_works":["https://openalex.org/W2042777683","https://openalex.org/W2166198789","https://openalex.org/W1975173385","https://openalex.org/W4213388528","https://openalex.org/W2078643856","https://openalex.org/W2061934839","https://openalex.org/W4232100110","https://openalex.org/W1537420147","https://openalex.org/W2069557654","https://openalex.org/W2071623365"],"abstract_inverted_index":{"Considerable":[0],"evidence":[1],"suggests":[2],"that":[3,65],"in":[4],"complex":[5],"diseases":[6],"the":[7,50,80],"deteriorations":[8],"are":[9],"often":[10],"abrupt,":[11],"and":[12],"can":[13],"be":[14],"viewed":[15],"as":[16,67],"a":[17,20,32,68,99,116],"bifurcation":[18,75],"or":[19,76],"critical":[21,47,81,110],"transition":[22,82],"from":[23,49,115],"one":[24,30],"asymptotically":[25],"stable":[26],"equilibrium":[27],"to":[28,41,102],"another":[29],"at":[31],"tipping":[33],"point.":[34],"Here,":[35],"we":[36,60,85],"propose":[37],"some":[38],"new":[39,104,117],"ideas":[40],"detect":[42],"early-warning":[43,70],"signals":[44],"of":[45,52,55,112],"such":[46],"transitions":[48,111],"perspective":[51],"qualitative":[53],"theory":[54],"ordinary":[56],"differential":[57],"equations.":[58],"Specifically,":[59],"theoretically":[61],"derive":[62],"three":[63,94],"indicators":[64],"serve":[66],"general":[69],"signal":[71],"indicating":[72],"an":[73],"imminent":[74],"sudden":[77],"deterioration":[78],"before":[79],"occurs.":[83],"Then,":[84],"verify":[86],"our":[87],"theoretical":[88],"results":[89],"by":[90],"numerical":[91],"simulations":[92],"for":[93,109],"examples.":[95],"Our":[96],"work":[97],"forms":[98],"starting":[100],"point":[101],"motivate":[103],"mathematical":[105],"insights":[106],"into":[107],"predictability":[108],"dynamical":[113],"systems":[114],"perspective.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}