{"id":"https://openalex.org/W2252696324","doi":"https://doi.org/10.1142/s0218127415501102","title":"Qualitative Analysis of a Predator\u2013Prey Model with Crowley\u2013Martin Functional Response","display_name":"Qualitative Analysis of a Predator\u2013Prey Model with Crowley\u2013Martin Functional Response","publication_year":2015,"publication_date":"2015-08-01","ids":{"openalex":"https://openalex.org/W2252696324","doi":"https://doi.org/10.1142/s0218127415501102","mag":"2252696324"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127415501102","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415501102","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/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaying Dong","raw_affiliation_strings":["School of Mathematics, Northwest University, Xi'an, Shaanxi 710069, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Northwest University, Xi'an, Shaanxi 710069, P. R. China","institution_ids":["https://openalex.org/I37802460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101833857","display_name":"Shunli Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shunli Zhang","raw_affiliation_strings":["School of Mathematics, Northwest University, Xi'an, Shaanxi 710069, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Northwest University, Xi'an, Shaanxi 710069, P. R. China","institution_ids":["https://openalex.org/I37802460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040396119","display_name":"Shanbing Li","orcid":"https://orcid.org/0000-0002-6994-0952"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shanbing Li","raw_affiliation_strings":["College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101944007","display_name":"LI Yan-ling","orcid":"https://orcid.org/0000-0002-9614-4927"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanling Li","raw_affiliation_strings":["College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040396119"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":2.3024,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.88562493,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"09","first_page":"1550110","last_page":"1550110"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9907000064849854,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.807537317276001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.766727864742279},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.7477739453315735},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.5800231099128723},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5453166961669922},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.544198215007782},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4712182581424713},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4333406388759613},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.41597533226013184},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3846900165081024},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3821428120136261},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.3787173330783844},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3784034848213196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11278262734413147},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.08808338642120361},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07548332214355469}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.807537317276001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.766727864742279},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.7477739453315735},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.5800231099128723},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5453166961669922},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.544198215007782},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4712182581424713},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4333406388759613},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.41597533226013184},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3846900165081024},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3821428120136261},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.3787173330783844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3784034848213196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11278262734413147},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.08808338642120361},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07548332214355469},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/s0218127415501102","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415501102","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1550364336","https://openalex.org/W1827761481","https://openalex.org/W1983335260","https://openalex.org/W1984884374","https://openalex.org/W1993286500","https://openalex.org/W2025516574","https://openalex.org/W2026753738","https://openalex.org/W2029879748","https://openalex.org/W2038105662","https://openalex.org/W2053374006","https://openalex.org/W2065356152","https://openalex.org/W2065736324","https://openalex.org/W2069349885","https://openalex.org/W2074603814","https://openalex.org/W2092696532","https://openalex.org/W2093957401","https://openalex.org/W2108337779","https://openalex.org/W2123261528","https://openalex.org/W2143336666","https://openalex.org/W2153573574","https://openalex.org/W4312587821"],"related_works":["https://openalex.org/W4233887507","https://openalex.org/W2061879675","https://openalex.org/W2084621533","https://openalex.org/W2077303587","https://openalex.org/W2059261737","https://openalex.org/W2054969521","https://openalex.org/W3033051025","https://openalex.org/W3194003107","https://openalex.org/W2039016328","https://openalex.org/W2796513049"],"abstract_inverted_index":{"In":[0,55],"this":[1],"paper,":[2],"we":[3,23,40,57,75,90],"are":[4],"concerned":[5],"with":[6,13],"positive":[7,33,48,67,84],"solutions":[8,34,49,68,85],"of":[9,31,46,65,82],"a":[10,51],"predator\u2013prey":[11],"model":[12],"Crowley\u2013Martin":[14],"functional":[15],"response":[16],"under":[17],"homogeneous":[18],"Dirichlet":[19],"boundary":[20],"conditions.":[21],"First,":[22],"prove":[24],"the":[25,29,32,42,47,63,66,77,87,97],"existence":[26],"and":[27,44,79],"reveal":[28],"structure":[30],"by":[35,69],"using":[36,70],"bifurcation":[37],"theory.":[38],"Then,":[39],"investigate":[41],"uniqueness":[43,64],"stability":[45],"for":[50,62],"large":[52],"key":[53],"parameter.":[54],"addition,":[56],"derive":[58],"some":[59,71,92],"sufficient":[60],"conditions":[61],"specific":[72],"inequalities.":[73],"Moreover,":[74],"discuss":[76],"extinction":[78],"persistence":[80],"results":[81,99],"time-dependent":[83],"to":[86,95],"system.":[88],"Finally,":[89],"present":[91],"numerical":[93],"simulations":[94],"supplement":[96],"analytic":[98],"in":[100],"one":[101],"dimension.":[102]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}