{"id":"https://openalex.org/W7134070247","doi":"https://doi.org/10.1016/j.jfranklin.2026.108573","title":"Dynamics analysis of a food chain chemostat model with flocculation and diffusion effects","display_name":"Dynamics analysis of a food chain chemostat model with flocculation and diffusion effects","publication_year":2026,"publication_date":"2026-03-06","ids":{"openalex":"https://openalex.org/W7134070247","doi":"https://doi.org/10.1016/j.jfranklin.2026.108573"},"language":"en","primary_location":{"id":"doi:10.1016/j.jfranklin.2026.108573","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jfranklin.2026.108573","pdf_url":null,"source":{"id":"https://openalex.org/S183498172","display_name":"Journal of the Franklin Institute","issn_l":"0016-0032","issn":["0016-0032","1879-2693"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Franklin Institute","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":null,"display_name":"Xin Xu","orcid":"https://orcid.org/0009-0005-8367-942X"},"institutions":[{"id":"https://openalex.org/I1297991670","display_name":"Southwest University of Science and Technology","ror":"https://ror.org/04d996474","country_code":"CN","type":"education","lineage":["https://openalex.org/I1297991670"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Xu","raw_affiliation_strings":["School of Mathematics and Physics, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China"],"raw_orcid":"https://orcid.org/0009-0005-8367-942X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China","institution_ids":["https://openalex.org/I1297991670"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087441398","display_name":"Baodan Tian","orcid":"https://orcid.org/0000-0003-1109-958X"},"institutions":[{"id":"https://openalex.org/I1297991670","display_name":"Southwest University of Science and Technology","ror":"https://ror.org/04d996474","country_code":"CN","type":"education","lineage":["https://openalex.org/I1297991670"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Baodan Tian","raw_affiliation_strings":["Institute of Data Model Algorithms, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China","School of Mathematics and Physics, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China"],"raw_orcid":"https://orcid.org/0000-0003-1109-958X","affiliations":[{"raw_affiliation_string":"Institute of Data Model Algorithms, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China","institution_ids":["https://openalex.org/I1297991670"]},{"raw_affiliation_string":"School of Mathematics and Physics, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China","institution_ids":["https://openalex.org/I1297991670"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069321666","display_name":"Yanhong Qiu","orcid":"https://orcid.org/0000-0003-0921-5254"},"institutions":[{"id":"https://openalex.org/I1297991670","display_name":"Southwest University of Science and Technology","ror":"https://ror.org/04d996474","country_code":"CN","type":"education","lineage":["https://openalex.org/I1297991670"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanhong Qiu","raw_affiliation_strings":["School of Mathematics and Physics, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China"],"raw_orcid":"https://orcid.org/0000-0003-0921-5254","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Southwest University of Science and Technology, Sichuan, Mianyang, 621010, PR China","institution_ids":["https://openalex.org/I1297991670"]}]},{"author_position":"last","author":{"id":null,"display_name":"Hailing Wang","orcid":"https://orcid.org/0000-0003-0333-5044"},"institutions":[{"id":"https://openalex.org/I29739308","display_name":"Guangxi Normal University","ror":"https://ror.org/02frt9q65","country_code":"CN","type":"education","lineage":["https://openalex.org/I29739308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hailing Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Guangxi Normal University, Guangxi, Guilin, 541006, PR China"],"raw_orcid":"https://orcid.org/0000-0003-0333-5044","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guangxi Normal University, Guangxi, Guilin, 541006, PR China","institution_ids":["https://openalex.org/I29739308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087441398"],"corresponding_institution_ids":["https://openalex.org/I1297991670"],"apc_list":{"value":2700,"currency":"USD","value_usd":2700},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24032716,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"363","issue":"7","first_page":"108573","last_page":"108573"},"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":0.9664999842643738,"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":0.9664999842643738,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.014000000432133675,"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/T11188","display_name":"Coagulation and Flocculation Studies","score":0.003100000089034438,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"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/chemostat","display_name":"Chemostat","score":0.9007999897003174},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6274999976158142},{"id":"https://openalex.org/keywords/flocculation","display_name":"Flocculation","score":0.5867999792098999},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5336999893188477},{"id":"https://openalex.org/keywords/growth-rate","display_name":"Growth rate","score":0.49720001220703125},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.446399986743927},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.43849998712539673},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43619999289512634}],"concepts":[{"id":"https://openalex.org/C125111812","wikidata":"https://www.wikidata.org/wiki/Q902311","display_name":"Chemostat","level":3,"score":0.9007999897003174},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6274999976158142},{"id":"https://openalex.org/C148815931","wikidata":"https://www.wikidata.org/wiki/Q900689","display_name":"Flocculation","level":2,"score":0.5867999792098999},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5839999914169312},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5336999893188477},{"id":"https://openalex.org/C2778312390","wikidata":"https://www.wikidata.org/wiki/Q4139973","display_name":"Growth rate","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.4562999904155731},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.446399986743927},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.43849998712539673},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43619999289512634},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.4108999967575073},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39640000462532043},{"id":"https://openalex.org/C155373166","wikidata":"https://www.wikidata.org/wiki/Q159462","display_name":"Food chain","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.335099995136261},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.31349998712539673},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.2913999855518341},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.28380000591278076},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2711000144481659},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.2655999958515167},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jfranklin.2026.108573","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jfranklin.2026.108573","pdf_url":null,"source":{"id":"https://openalex.org/S183498172","display_name":"Journal of the Franklin Institute","issn_l":"0016-0032","issn":["0016-0032","1879-2693"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Franklin Institute","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/2","score":0.5063300728797913,"display_name":"Zero hunger"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322559","display_name":"Southwest University of Science and Technology","ror":"https://ror.org/04d996474"},{"id":"https://openalex.org/F4320322922","display_name":"Department of Science and Technology of Sichuan Province","ror":"https://ror.org/04323m874"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1955491099","https://openalex.org/W1963642114","https://openalex.org/W1964633266","https://openalex.org/W1966552169","https://openalex.org/W1976999354","https://openalex.org/W1979472394","https://openalex.org/W1991899745","https://openalex.org/W2001067070","https://openalex.org/W2003672769","https://openalex.org/W2010231803","https://openalex.org/W2019619617","https://openalex.org/W2019635403","https://openalex.org/W2020870487","https://openalex.org/W2024993041","https://openalex.org/W2025846683","https://openalex.org/W2039365029","https://openalex.org/W2046724040","https://openalex.org/W2053581978","https://openalex.org/W2060524950","https://openalex.org/W2064728990","https://openalex.org/W2074729902","https://openalex.org/W2074921524","https://openalex.org/W2094247338","https://openalex.org/W2096356504","https://openalex.org/W2112836364","https://openalex.org/W2125914782","https://openalex.org/W2157935118","https://openalex.org/W2315708885","https://openalex.org/W2338367111","https://openalex.org/W2606585350","https://openalex.org/W2921741176","https://openalex.org/W3182657164","https://openalex.org/W4280497188","https://openalex.org/W4309636939","https://openalex.org/W4395701748","https://openalex.org/W4400844343","https://openalex.org/W4403464311"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2026-03-07T00:00:00"}
