{"id":"https://openalex.org/W2500987249","doi":"https://doi.org/10.1142/s0218127416500887","title":"Spatiotemporal Patterns of a Predator\u2013Prey System with an Allee Effect and Holling Type III Functional Response","display_name":"Spatiotemporal Patterns of a Predator\u2013Prey System with an Allee Effect and Holling Type III Functional Response","publication_year":2016,"publication_date":"2016-05-01","ids":{"openalex":"https://openalex.org/W2500987249","doi":"https://doi.org/10.1142/s0218127416500887","mag":"2500987249"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500887","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500887","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/A5101573445","display_name":"Yuanyuan Li","orcid":"https://orcid.org/0000-0002-9143-8029"},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanyuan Li","raw_affiliation_strings":["School of Mathematical Science, Harbin Normal University, Harbin 150025, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Harbin Normal University, Harbin 150025, P. R. China","institution_ids":["https://openalex.org/I134052481"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100344674","display_name":"Jinfeng Wang","orcid":"https://orcid.org/0000-0002-0103-163X"},"institutions":[{"id":"https://openalex.org/I134052481","display_name":"Harbin Normal University","ror":"https://ror.org/0270y6950","country_code":"CN","type":"education","lineage":["https://openalex.org/I134052481"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinfeng Wang","raw_affiliation_strings":["School of Mathematical Science, Harbin Normal University, Harbin 150025, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Harbin Normal University, Harbin 150025, P. R. China","institution_ids":["https://openalex.org/I134052481"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100344674"],"corresponding_institution_ids":["https://openalex.org/I134052481"],"apc_list":null,"apc_paid":null,"fwci":1.1493,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82863624,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"05","first_page":"1650088","last_page":"1650088"},"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9700000286102295,"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/allee-effect","display_name":"Allee effect","score":0.9541975259780884},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.7675193548202515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7380726933479309},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5977550745010376},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.5869973301887512},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4971943199634552},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.46050119400024414},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4539080858230591},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.44625478982925415},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.4446563720703125},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.42989516258239746},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42725902795791626},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.386268675327301},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3577881455421448},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35571107268333435},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.2598193883895874},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2058444321155548},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10419854521751404},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.10132390260696411},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08374837040901184},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.07522964477539062},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0706358551979065}],"concepts":[{"id":"https://openalex.org/C10958125","wikidata":"https://www.wikidata.org/wiki/Q2301505","display_name":"Allee effect","level":3,"score":0.9541975259780884},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.7675193548202515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7380726933479309},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5977550745010376},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5869973301887512},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4971943199634552},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.46050119400024414},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4539080858230591},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.44625478982925415},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.4446563720703125},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.42989516258239746},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42725902795791626},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.386268675327301},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3577881455421448},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35571107268333435},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.2598193883895874},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2058444321155548},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10419854521751404},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.10132390260696411},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08374837040901184},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.07522964477539062},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0706358551979065},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","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/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416500887","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500887","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":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.5899999737739563}],"awards":[{"id":"https://openalex.org/G2155741408","display_name":null,"funder_award_id":"11201101","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":39,"referenced_works":["https://openalex.org/W1550364336","https://openalex.org/W1560060148","https://openalex.org/W1604719947","https://openalex.org/W1966280076","https://openalex.org/W1968422033","https://openalex.org/W1983575156","https://openalex.org/W1986023394","https://openalex.org/W1992529385","https://openalex.org/W1997882516","https://openalex.org/W1998822018","https://openalex.org/W2001024435","https://openalex.org/W2005697843","https://openalex.org/W2020870487","https://openalex.org/W2021944024","https://openalex.org/W2029989964","https://openalex.org/W2038105662","https://openalex.org/W2039005786","https://openalex.org/W2041263000","https://openalex.org/W2044266995","https://openalex.org/W2046417763","https://openalex.org/W2058877262","https://openalex.org/W2064614958","https://openalex.org/W2065029966","https://openalex.org/W2067183512","https://openalex.org/W2067748671","https://openalex.org/W2069772140","https://openalex.org/W2072682643","https://openalex.org/W2074915596","https://openalex.org/W2086793470","https://openalex.org/W2093957401","https://openalex.org/W2105939751","https://openalex.org/W2107190886","https://openalex.org/W2112624608","https://openalex.org/W2114054963","https://openalex.org/W2131915744","https://openalex.org/W2132246068","https://openalex.org/W2323729682","https://openalex.org/W2333257432","https://openalex.org/W2335720253"],"related_works":["https://openalex.org/W2954520391","https://openalex.org/W3160246123","https://openalex.org/W4309891670","https://openalex.org/W4390448314","https://openalex.org/W4367180708","https://openalex.org/W3194217620","https://openalex.org/W2963652880","https://openalex.org/W4292054940","https://openalex.org/W2957281485","https://openalex.org/W2364474991"],"abstract_inverted_index":{"A":[0],"diffusive":[1],"Gause":[2],"type":[3,14],"predator\u2013prey":[4],"system":[5,48],"with":[6],"Allee":[7],"effect":[8],"in":[9],"prey":[10],"growth":[11],"and":[12,37,57],"Holling":[13],"III":[15],"response":[16],"subject":[17],"to":[18],"Neumann":[19],"boundary":[20],"conditions":[21],"is":[22,31,49],"investigated.":[23,51],"Existence":[24],"of":[25,42,46,54],"nonconstant":[26],"positive":[27,44],"steady":[28],"state":[29],"solutions":[30,60],"proved":[32],"by":[33],"Leray\u2013Schauder":[34],"degree":[35],"theory":[36],"bifurcation":[38],"theory.":[39],"Global":[40],"stability":[41],"the":[43,47],"equilibrium":[45],"also":[50],"Moreover,":[52],"bifurcations":[53],"spatially":[55],"homogeneous":[56],"nonhomogeneous":[58],"periodic":[59],"are":[61],"analyzed.":[62],"Our":[63],"rigorous":[64],"results":[65],"justify":[66],"some":[67],"recent":[68],"ecological":[69],"observations.":[70]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
