{"id":"https://openalex.org/W4410856293","doi":"https://doi.org/10.1142/s0218127425501093","title":"Turing Instability of Periodic Solutions and Stationary Patterns Induced by Cross-Diffusion in a Holling Type-II Prey\u2013Predator Model","display_name":"Turing Instability of Periodic Solutions and Stationary Patterns Induced by Cross-Diffusion in a Holling Type-II Prey\u2013Predator Model","publication_year":2025,"publication_date":"2025-05-29","ids":{"openalex":"https://openalex.org/W4410856293","doi":"https://doi.org/10.1142/s0218127425501093"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425501093","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501093","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/A5100527322","display_name":"Tian Shu","orcid":null},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shu Tian","raw_affiliation_strings":["Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, P.\u00a0R.\u00a0China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I68986083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100527322"],"corresponding_institution_ids":["https://openalex.org/I68986083"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19884471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"09","first_page":null,"last_page":null},"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":0.9951000213623047,"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":0.9951000213623047,"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":0.991599977016449,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9553999900817871,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.6941719055175781},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.6488378047943115},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.636578381061554},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.6265953183174133},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5717822313308716},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.535564124584198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4945068061351776},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.46336811780929565},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3900585174560547},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3531595468521118},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33728092908859253},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32518476247787476},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20272529125213623},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.19249460101127625},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.1694466769695282},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.16065040230751038},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06339618563652039}],"concepts":[{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.6941719055175781},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.6488378047943115},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.636578381061554},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.6265953183174133},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5717822313308716},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.535564124584198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4945068061351776},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.46336811780929565},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3900585174560547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3531595468521118},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33728092908859253},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32518476247787476},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20272529125213623},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.19249460101127625},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.1694466769695282},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.16065040230751038},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06339618563652039},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127425501093","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501093","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1969527372","https://openalex.org/W1974301594","https://openalex.org/W1980661496","https://openalex.org/W1983575156","https://openalex.org/W1984409514","https://openalex.org/W1986023394","https://openalex.org/W1989971796","https://openalex.org/W1997882516","https://openalex.org/W2005132309","https://openalex.org/W2011067252","https://openalex.org/W2038105662","https://openalex.org/W2043713410","https://openalex.org/W2047781060","https://openalex.org/W2052125279","https://openalex.org/W2060665770","https://openalex.org/W2065355448","https://openalex.org/W2066496593","https://openalex.org/W2094247338","https://openalex.org/W2125914782","https://openalex.org/W2132996211","https://openalex.org/W2525152882","https://openalex.org/W2603374957","https://openalex.org/W2663723497","https://openalex.org/W3004107098","https://openalex.org/W3126404422","https://openalex.org/W4214500652","https://openalex.org/W4236990395","https://openalex.org/W4247319733","https://openalex.org/W4313315635","https://openalex.org/W4385603514","https://openalex.org/W4390903438","https://openalex.org/W4394619626"],"related_works":["https://openalex.org/W2168669462","https://openalex.org/W4233887507","https://openalex.org/W2061879675","https://openalex.org/W2192426841","https://openalex.org/W2067000585","https://openalex.org/W4323811225","https://openalex.org/W2164070575","https://openalex.org/W4311356582","https://openalex.org/W2163677464","https://openalex.org/W2103498027"],"abstract_inverted_index":{"In":[0,120],"this":[1],"paper,":[2],"we":[3,132],"consider":[4],"a":[5,27,150,169],"Holling":[6],"type-II":[7],"prey\u2013predator":[8],"model":[9,25],"with":[10],"cross-diffusion":[11,91,148],"under":[12,95],"homogeneous":[13,42],"Neumann":[14],"boundary":[15],"conditions.":[16],"The":[17],"existing":[18],"literature":[19],"shows":[20],"that":[21,51,94,115,147,159],"the":[22,46,67,69,76,90,98,124,137,154,173],"corresponding":[23],"ODE":[24],"admits":[26],"unique":[28],"globally":[29],"asymptotically":[30,40],"stable":[31,41],"periodic":[32,36,43,60,73,99,109],"solutions":[33,37,44,74,82,100,110],"and":[34,75,129],"these":[35,96],"become":[38],"locally":[39],"in":[45,66,153],"diffusive":[47],"model,":[48,68],"which":[49,167],"means":[50],"passive":[52],"diffusion":[53],"does":[54],"not":[55],"create":[56,163],"Turing":[57,70,103,106],"instability":[58,71,107],"of":[59,72,78,108,139,156],"solutions.":[61,143],"When":[62],"cross-diffusions":[63],"are":[64,83],"introduced":[65],"existence":[77,138],"nonconstant":[79,140],"positive":[80,141],"stationary":[81,142],"studied.":[84],"We":[85],"derive":[86],"exact":[87],"conditions":[88,135],"on":[89],"coefficients":[92],"so":[93],"conditions,":[97],"can":[101,162],"undergo":[102],"instability.":[104],"Once":[105],"occurs,":[111],"numerical":[112],"simulations":[113],"show":[114,146],"new":[116,164],"irregular":[117,165],"patterns":[118],"emerge.":[119],"addition,":[121],"by":[122],"using":[123],"fixed":[125],"point":[126],"index":[127],"theory":[128],"analytical":[130],"techniques,":[131],"obtain":[133],"sufficient":[134],"for":[136],"Our":[144],"results":[145],"plays":[149],"crucial":[151],"role":[152],"formation":[155],"spatiotemporal":[157],"patterns,":[158,166],"is,":[160],"it":[161],"is":[168],"sharp":[170],"contrast":[171],"to":[172],"case":[174],"without":[175],"cross-diffusion.":[176]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}