{"id":"https://openalex.org/W3011843610","doi":"https://doi.org/10.1142/s0218127420500248","title":"Bifurcation Analysis in a Cancer Growth Model","display_name":"Bifurcation Analysis in a Cancer Growth Model","publication_year":2020,"publication_date":"2020-02-01","ids":{"openalex":"https://openalex.org/W3011843610","doi":"https://doi.org/10.1142/s0218127420500248","mag":"3011843610"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420500248","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420500248","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/A5101700751","display_name":"Yu Chang","orcid":"https://orcid.org/0000-0001-5572-467X"},"institutions":[{"id":"https://openalex.org/I75390827","display_name":"Beijing University of Chemical Technology","ror":"https://ror.org/00df5yc52","country_code":"CN","type":"education","lineage":["https://openalex.org/I75390827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu Chang","raw_affiliation_strings":["College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-5572-467X","affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. China","institution_ids":["https://openalex.org/I75390827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100456937","display_name":"Xiaoli Wang","orcid":"https://orcid.org/0009-0009-6430-8673"},"institutions":[{"id":"https://openalex.org/I75390827","display_name":"Beijing University of Chemical Technology","ror":"https://ror.org/00df5yc52","country_code":"CN","type":"education","lineage":["https://openalex.org/I75390827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoli Wang","raw_affiliation_strings":["College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. China","institution_ids":["https://openalex.org/I75390827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100294700","display_name":"Zhihong Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090512","display_name":"Guangzhou Experimental Station","ror":"https://ror.org/00f2c2516","country_code":"CN","type":"facility","lineage":["https://openalex.org/I107851509","https://openalex.org/I4210090512","https://openalex.org/I4210127390","https://openalex.org/I4210151987"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhihong Feng","raw_affiliation_strings":["Guangzhou Middle School, Guangzhou, Guangdong Province 510640, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangzhou Middle School, Guangzhou, Guangdong Province 510640, P. R. China","institution_ids":["https://openalex.org/I4210090512"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100628391","display_name":"Wei Feng","orcid":"https://orcid.org/0000-0002-5244-1452"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Feng","raw_affiliation_strings":["LMIB and School of Mathematics and System Sciences, Beihang University, Beijing 100083, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB and School of Mathematics and System Sciences, Beihang University, Beijing 100083, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101700751"],"corresponding_institution_ids":["https://openalex.org/I75390827"],"apc_list":null,"apc_paid":null,"fwci":0.1403,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.52870216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"02","first_page":"2050024","last_page":"2050024"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9932000041007996,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9800999760627747,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.7539048194885254},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.751599907875061},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.724579930305481},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7095538377761841},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6532578468322754},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.5715237259864807},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.5613232851028442},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5547319650650024},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.5445743203163147},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.5441166162490845},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.4460434317588806},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3960665762424469},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35411763191223145},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2844201326370239},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20396488904953003}],"concepts":[{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.7539048194885254},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.751599907875061},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.724579930305481},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7095538377761841},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6532578468322754},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.5715237259864807},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.5613232851028442},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5547319650650024},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.5445743203163147},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.5441166162490845},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.4460434317588806},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3960665762424469},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35411763191223145},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2844201326370239},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20396488904953003},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127420500248","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420500248","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":[{"id":"https://openalex.org/G6382656475","display_name":null,"funder_award_id":"11771033","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W196418234","https://openalex.org/W621027901","https://openalex.org/W1944556400","https://openalex.org/W1966972548","https://openalex.org/W1984613448","https://openalex.org/W2013304036","https://openalex.org/W2020441022","https://openalex.org/W2027065943","https://openalex.org/W2040429438","https://openalex.org/W2041777499","https://openalex.org/W2058763139","https://openalex.org/W2070614679","https://openalex.org/W2106721944","https://openalex.org/W2107760337","https://openalex.org/W2141977078","https://openalex.org/W2166355248","https://openalex.org/W2172166318","https://openalex.org/W2297521577","https://openalex.org/W2692842713","https://openalex.org/W4294967943"],"related_works":["https://openalex.org/W2356715721","https://openalex.org/W2049615654","https://openalex.org/W2267377916","https://openalex.org/W2025138898","https://openalex.org/W1982778171","https://openalex.org/W2923981205","https://openalex.org/W2775656422","https://openalex.org/W2054075447","https://openalex.org/W2028337061","https://openalex.org/W2312845532"],"abstract_inverted_index":{"A":[0],"mathematical":[1],"model":[2],"describing":[3],"interactions":[4],"among":[5],"tumor":[6],"cells,":[7],"healthy":[8],"host":[9],"cells":[10,13],"and":[11,30,63,70,87,101,114],"immune":[12],"is":[14,47],"extensively":[15],"investigated":[16],"through":[17],"bifurcation":[18,26,29,32,46],"analysis":[19],"with":[20],"all":[21],"parameters":[22],"fixed":[23],"except":[24],"one":[25],"parameter.":[27],"Transcritical":[28],"saddle-node":[31],"are":[33,77],"studied":[34],"in":[35,49],"the":[36,41,50,55,61,64,67,71,88,112,121,125],"vector":[37],"fields":[38],"restricted":[39],"to":[40,60,116],"corresponding":[42],"center":[43],"manifolds.":[44],"Hopf":[45],"analyzed":[48],"frequency":[51,62],"domain.":[52],"In":[53],"particular,":[54],"sixth-order":[56],"harmonic":[57],"balance":[58],"approximations":[59],"amplitude":[65],"of":[66,85,120,124],"periodic":[68],"solutions,":[69],"analytical":[72],"expressions":[73],"for":[74],"these":[75,105],"solutions":[76],"given.":[78],"Numerical":[79],"simulation":[80],"study":[81],"demonstrates":[82],"various":[83],"types":[84],"bifurcations":[86],"complex":[89],"solution":[90],"behaviors,":[91],"such":[92],"as":[93],"cyclic":[94],"fold":[95],"bifurcation,":[96,98],"period-doubling":[97,99],"cascade":[100],"chaotic":[102],"orbits.":[103],"All":[104],"results":[106],"complement":[107],"previous":[108],"theoretical":[109],"studies":[110],"on":[111],"model,":[113],"contribute":[115],"a":[117],"better":[118],"understanding":[119],"qualitative":[122],"dynamics":[123],"cancer":[126],"model.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
