{"id":"https://openalex.org/W3096302683","doi":"https://doi.org/10.1142/s0218127420501825","title":"Global Bifurcation of Stationary Solutions for a Volume-Filling Chemotaxis Model with Logistic Growth","display_name":"Global Bifurcation of Stationary Solutions for a Volume-Filling Chemotaxis Model with Logistic Growth","publication_year":2020,"publication_date":"2020-10-01","ids":{"openalex":"https://openalex.org/W3096302683","doi":"https://doi.org/10.1142/s0218127420501825","mag":"3096302683"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420501825","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501825","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/A5042167439","display_name":"Yaying Dong","orcid":null},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaying Dong","raw_affiliation_strings":["School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, P. R. China","institution_ids":["https://openalex.org/I27599042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040396119","display_name":"Shanbing Li","orcid":"https://orcid.org/0000-0002-6994-0952"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shanbing Li","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi\u2019an 710071, P. R China"],"raw_orcid":"https://orcid.org/0000-0002-6994-0952","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi\u2019an 710071, P. R China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08979439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"13","first_page":"2050182","last_page":"2050182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"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":1.0,"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/T10379","display_name":"Cellular Mechanics and Interactions","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell 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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9742000102996826,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7524878978729248},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7104201912879944},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.583600640296936},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5563084483146667},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.5387789607048035},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.53508061170578},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.46067556738853455},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.42043042182922363},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38707542419433594},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3816567659378052},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.132938951253891},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05637311935424805}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7524878978729248},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7104201912879944},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.583600640296936},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5563084483146667},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5387789607048035},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.53508061170578},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.46067556738853455},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.42043042182922363},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38707542419433594},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3816567659378052},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.132938951253891},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05637311935424805},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","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/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/s0218127420501825","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501825","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/G3409179726","display_name":null,"funder_award_id":"2018JQ1017","funder_id":"https://openalex.org/F4320324173","funder_display_name":"Natural Science Foundation of Shaanxi Province"},{"id":"https://openalex.org/G3656058072","display_name":null,"funder_award_id":"2018JQ1004","funder_id":"https://openalex.org/F4320324173","funder_display_name":"Natural Science Foundation of Shaanxi Province"},{"id":"https://openalex.org/G6031165059","display_name":null,"funder_award_id":"2018T111014","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6906855610","display_name":null,"funder_award_id":"2018M631133","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8527287743","display_name":null,"funder_award_id":"11801431","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"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320324173","display_name":"Natural Science Foundation of Shaanxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1767076154","https://openalex.org/W1981138250","https://openalex.org/W1987347396","https://openalex.org/W1995485163","https://openalex.org/W1995794459","https://openalex.org/W2020870487","https://openalex.org/W2021117151","https://openalex.org/W2021175251","https://openalex.org/W2023884962","https://openalex.org/W2025502057","https://openalex.org/W2040380154","https://openalex.org/W2042892258","https://openalex.org/W2044391638","https://openalex.org/W2046495918","https://openalex.org/W2049223241","https://openalex.org/W2055475190","https://openalex.org/W2055661993","https://openalex.org/W2056334019","https://openalex.org/W2065500531","https://openalex.org/W2068213416","https://openalex.org/W2092696532","https://openalex.org/W2093957401","https://openalex.org/W2153573574","https://openalex.org/W2168977801","https://openalex.org/W2169520590","https://openalex.org/W2224708578","https://openalex.org/W2252696324","https://openalex.org/W2305212917","https://openalex.org/W2460465955","https://openalex.org/W2587611072","https://openalex.org/W4237997615"],"related_works":["https://openalex.org/W2137413016","https://openalex.org/W2094046875","https://openalex.org/W110415256","https://openalex.org/W2069713792","https://openalex.org/W370258010","https://openalex.org/W4388906764","https://openalex.org/W2334634358","https://openalex.org/W2233462344","https://openalex.org/W2953100338","https://openalex.org/W2051166715"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,83],"show":[4,55],"how":[5],"the":[6,34,37,66,98,101,108],"global":[7,95],"bifurcation":[8,102],"theory":[9],"for":[10,22,41,78],"nonlinear":[11],"Fredholm":[12],"operators":[13,24],"(Theorem":[14,25],"4.3":[15],"of":[16,27,36,61,100],"[Shi":[17],"&":[18],"Wang,":[19],"2009])":[20],"and":[21,97],"compact":[23],"1.3":[26],"[Rabinowitz,":[28],"1971])":[29],"can":[30,90],"be":[31,91],"used":[32],"in":[33],"study":[35],"nonconstant":[38,62],"stationary":[39],"solutions":[40,63],"a":[42,94],"volume-filling":[43],"chemotaxis":[44],"model":[45],"with":[46],"logistic":[47],"growth":[48],"under":[49],"Neumann":[50],"boundary":[51],"conditions.":[52],"Our":[53],"results":[54],"that":[56,85],"infinitely":[57],"many":[58],"local":[59],"branches":[60],"bifurcate":[64],"from":[65],"positive":[67],"constant":[68],"solution":[69],"[Formula:":[70,74,80,87,104,109,113],"see":[71,75,81,88,105,110,114],"text]":[72,89,106],"at":[73],"text].":[76,115],"Moreover,":[77],"each":[79,86],"text],":[82],"prove":[84],"extended":[92],"into":[93],"curve,":[96],"projection":[99],"curve":[103],"onto":[107],"text]-axis":[111],"contains":[112]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}