{"id":"https://openalex.org/W2883710534","doi":"https://doi.org/10.1142/s021812741850089x","title":"Turing Instability and Hopf Bifurcation in a Modified Leslie\u2013Gower Predator\u2013Prey Model with Cross-Diffusion","display_name":"Turing Instability and Hopf Bifurcation in a Modified Leslie\u2013Gower Predator\u2013Prey Model with Cross-Diffusion","publication_year":2018,"publication_date":"2018-06-30","ids":{"openalex":"https://openalex.org/W2883710534","doi":"https://doi.org/10.1142/s021812741850089x","mag":"2883710534"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741850089x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741850089x","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/A5040853578","display_name":"Walid Abid","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131288","display_name":"National Engineering School of Tunis","ror":"https://ror.org/03b1zjt31","country_code":"TN","type":"education","lineage":["https://openalex.org/I4210131288","https://openalex.org/I63596082"]},{"id":"https://openalex.org/I63596082","display_name":"Tunis El Manar University","ror":"https://ror.org/029cgt552","country_code":"TN","type":"education","lineage":["https://openalex.org/I63596082"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Walid Abid","raw_affiliation_strings":["University of Tunis El Manar, National Engineering School of Tunis, Laboratory of Engineering Mathematics EPT, BP 743, La Marsa 2078, Tunisia"],"affiliations":[{"raw_affiliation_string":"University of Tunis El Manar, National Engineering School of Tunis, Laboratory of Engineering Mathematics EPT, BP 743, La Marsa 2078, Tunisia","institution_ids":["https://openalex.org/I4210131288","https://openalex.org/I63596082"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016073934","display_name":"Radouane Yafia","orcid":"https://orcid.org/0000-0002-9824-9036"},"institutions":[{"id":"https://openalex.org/I4210088687","display_name":"Universit\u00e9 Ibn Zohr","ror":"https://ror.org/006sgpv47","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210088687"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"R. Yafia","raw_affiliation_strings":["Universit\u00e9 Ibn Zohr, BP 32/S, CP 80000 Agadir, Morocco"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Ibn Zohr, BP 32/S, CP 80000 Agadir, Morocco","institution_ids":["https://openalex.org/I4210088687"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036156842","display_name":"M. A. Aziz-Alaoui","orcid":"https://orcid.org/0000-0001-5198-4597"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I141576021","display_name":"Universit\u00e9 Le Havre Normandie","ror":"https://ror.org/05v509s40","country_code":"FR","type":"education","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4392021130","display_name":"Laboratoire de Math\u00e9matiques Appliqu\u00e9es du Havre","ror":"https://ror.org/017vnhv07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4392021130"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. A. Aziz-Alaoui","raw_affiliation_strings":["LMAH, FR-CNRS-3335, Universit\u00e9 du Havre Normandie, 25 Rue Ph. Lebon, BP 540, 76058 Le Havre Cedex, (Normandie) France"],"affiliations":[{"raw_affiliation_string":"LMAH, FR-CNRS-3335, Universit\u00e9 du Havre Normandie, 25 Rue Ph. Lebon, BP 540, 76058 Le Havre Cedex, (Normandie) France","institution_ids":["https://openalex.org/I4392021130","https://openalex.org/I141576021","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074386593","display_name":"Ahmed Aghriche","orcid":"https://orcid.org/0000-0003-2226-8430"},"institutions":[{"id":"https://openalex.org/I4210088687","display_name":"Universit\u00e9 Ibn Zohr","ror":"https://ror.org/006sgpv47","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210088687"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Ahmed Aghriche","raw_affiliation_strings":["Universit\u00e9 Ibn Zohr, BP 32/S, CP 80000 Agadir, Morocco"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Ibn Zohr, BP 32/S, CP 80000 Agadir, Morocco","institution_ids":["https://openalex.org/I4210088687"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040853578"],"corresponding_institution_ids":["https://openalex.org/I4210131288","https://openalex.org/I63596082"],"apc_list":null,"apc_paid":null,"fwci":2.0697,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.86978051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"28","issue":"07","first_page":"1850089","last_page":"1850089"},"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":0.996999979019165,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7563397884368896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7098777890205383},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.6440589427947998},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.5458391904830933},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5235393047332764},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5217993259429932},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5214328169822693},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.42772629857063293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37899404764175415},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3458141088485718},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18824946880340576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15883657336235046},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12260901927947998},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07260170578956604}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7563397884368896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7098777890205383},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.6440589427947998},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5458391904830933},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5235393047332764},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5217993259429932},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5214328169822693},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.42772629857063293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37899404764175415},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3458141088485718},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18824946880340576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15883657336235046},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12260901927947998},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07260170578956604},{"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/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","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":2,"locations":[{"id":"doi:10.1142/s021812741850089x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741850089x","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"},{"id":"pmh:oai:HAL:hal-02436332v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02436332","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Bifurcation and Chaos, 2018, 28 (07), pp.1850089. &#x27E8;10.1142/S021812741850089X&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W223641994","https://openalex.org/W1560060148","https://openalex.org/W1973118029","https://openalex.org/W1977744212","https://openalex.org/W1980661496","https://openalex.org/W1983173496","https://openalex.org/W1984825430","https://openalex.org/W1997830348","https://openalex.org/W2001451047","https://openalex.org/W2004728046","https://openalex.org/W2008483105","https://openalex.org/W2010265353","https://openalex.org/W2019292700","https://openalex.org/W2021382636","https://openalex.org/W2029490924","https://openalex.org/W2030453979","https://openalex.org/W2040712046","https://openalex.org/W2045669912","https://openalex.org/W2052189521","https://openalex.org/W2057796887","https://openalex.org/W2066448162","https://openalex.org/W2081560871","https://openalex.org/W2096356504","https://openalex.org/W2105160112","https://openalex.org/W2131915744","https://openalex.org/W2156920703","https://openalex.org/W2157454707","https://openalex.org/W2162839328","https://openalex.org/W2193955221","https://openalex.org/W2268017670","https://openalex.org/W2280090374","https://openalex.org/W2316904041","https://openalex.org/W2329980545","https://openalex.org/W4230335115","https://openalex.org/W4250716583"],"related_works":["https://openalex.org/W2022300913","https://openalex.org/W1570780624","https://openalex.org/W14400985","https://openalex.org/W2322569264","https://openalex.org/W2093673119","https://openalex.org/W2257349530","https://openalex.org/W2077461433","https://openalex.org/W2083493576","https://openalex.org/W1657992821","https://openalex.org/W2317545320"],"abstract_inverted_index":{"This":[0,17],"paper":[1],"is":[2,37,122],"concerned":[3],"with":[4,15],"some":[5,98],"mathematical":[6],"analysis":[7],"and":[8,41,69,83,108],"numerical":[9,99],"aspects":[10],"of":[11,23,31,46,50,55,58,81],"a":[12,20,59,89],"reaction\u2013diffusion":[13],"system":[14,18],"cross-diffusion.":[16],"models":[19],"modified":[21],"version":[22],"Leslie\u2013Gower":[24],"functional":[25],"response":[26],"as":[27,29],"well":[28],"that":[30,120],"the":[32,43,47,51,76,79,126,131,135],"Holling-type":[33],"II.":[34],"Our":[35],"aim":[36],"to":[38,103,109,124,129],"investigate":[39],"theoretically":[40],"numerically":[42],"asymptotic":[44],"behavior":[45],"interior":[48],"equilibrium":[49],"model.":[52],"The":[53],"conditions":[54,80],"boundedness,":[56],"existence":[57],"positively":[60],"invariant":[61],"set":[62],"are":[63,72,92],"proved.":[64,93],"Criteria":[65],"for":[66],"local":[67],"stability/instability":[68],"global":[70],"stability":[71],"obtained.":[73],"By":[74],"using":[75],"bifurcation":[77,85],"theory,":[78],"Hopf":[82],"Turing":[84],"critical":[86],"lines":[87],"in":[88,101,134],"spatial":[90,132],"domain":[91],"Finally,":[94],"we":[95],"carry":[96],"out":[97],"simulations":[100],"order":[102],"support":[104],"our":[105],"theoretical":[106],"results":[107],"interpret":[110],"how":[111],"biological":[112],"processes":[113],"affect":[114],"spatiotemporal":[115],"pattern":[116],"formation":[117],"which":[118],"show":[119],"it":[121],"useful":[123],"use":[125],"predator\u2013prey":[127],"model":[128],"detect":[130],"dynamics":[133],"real":[136],"life.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
