{"id":"https://openalex.org/W3136864140","doi":"https://doi.org/10.1142/s0218127421500358","title":"Oscillatory and Stationary Patterns in a Diffusive Model with Delay Effect","display_name":"Oscillatory and Stationary Patterns in a Diffusive Model with Delay Effect","publication_year":2021,"publication_date":"2021-03-15","ids":{"openalex":"https://openalex.org/W3136864140","doi":"https://doi.org/10.1142/s0218127421500358","mag":"3136864140"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421500358","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500358","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/A5015369343","display_name":"Shangjiang Guo","orcid":"https://orcid.org/0000-0002-9114-5269"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shangjiang Guo","raw_affiliation_strings":["School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, P. R. China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074796852","display_name":"Shangzhi Li","orcid":"https://orcid.org/0000-0002-3328-6151"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shangzhi Li","raw_affiliation_strings":["School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, P. R. China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047475427","display_name":"Bounsanong Sounvoravong","orcid":null},"institutions":[{"id":"https://openalex.org/I43895496","display_name":"National University of Laos","ror":"https://ror.org/031xne895","country_code":"LA","type":"education","lineage":["https://openalex.org/I43895496"]}],"countries":["LA"],"is_corresponding":false,"raw_author_name":"Bounsanong Sounvoravong","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, National University of Laos, Vientiane Capital, DongDok Campus, P. O. Box 7322, Laos"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, National University of Laos, Vientiane Capital, DongDok Campus, P. O. Box 7322, Laos","institution_ids":["https://openalex.org/I43895496"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015369343"],"corresponding_institution_ids":["https://openalex.org/I3124059619"],"apc_list":null,"apc_paid":null,"fwci":2.4986,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.88712084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"31","issue":"03","first_page":"2150035","last_page":"2150035"},"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":0.9994000196456909,"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":0.9994000196456909,"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/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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.7674232125282288},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5775474905967712},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5611889362335205},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4985201358795166},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.45490795373916626},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4305744767189026},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35342997312545776},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.129145085811615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7674232125282288},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5775474905967712},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5611889362335205},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4985201358795166},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.45490795373916626},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4305744767189026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35342997312545776},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.129145085811615},{"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/s0218127421500358","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500358","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":[{"id":"https://openalex.org/G6480382428","display_name":null,"funder_award_id":"11671123","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":32,"referenced_works":["https://openalex.org/W237924264","https://openalex.org/W1518843801","https://openalex.org/W1531715726","https://openalex.org/W1552317631","https://openalex.org/W1605753492","https://openalex.org/W1822833310","https://openalex.org/W1965778005","https://openalex.org/W1968044585","https://openalex.org/W1970189994","https://openalex.org/W1986600971","https://openalex.org/W1989028519","https://openalex.org/W1993642582","https://openalex.org/W2024417170","https://openalex.org/W2049690269","https://openalex.org/W2049929575","https://openalex.org/W2058310516","https://openalex.org/W2059777391","https://openalex.org/W2087064550","https://openalex.org/W2152203759","https://openalex.org/W2162656842","https://openalex.org/W2593695471","https://openalex.org/W2607138426","https://openalex.org/W2739290268","https://openalex.org/W2977708622","https://openalex.org/W2991058485","https://openalex.org/W3011946293","https://openalex.org/W3021309707","https://openalex.org/W3022035939","https://openalex.org/W3036102550","https://openalex.org/W3047803552","https://openalex.org/W4211202937","https://openalex.org/W4300576184"],"related_works":["https://openalex.org/W2001036795","https://openalex.org/W2154748900","https://openalex.org/W2474979212","https://openalex.org/W3093811938","https://openalex.org/W1601247381","https://openalex.org/W127450631","https://openalex.org/W2062626603","https://openalex.org/W2087351849","https://openalex.org/W257950053","https://openalex.org/W2103804668"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,56],"reaction\u2013diffusion":[4],"model":[5],"with":[6,51,90],"delay":[7,106],"effect":[8,103],"and":[9,19,62,128],"Dirichlet":[10],"boundary":[11],"condition":[12],"is":[13,77],"considered.":[14],"Firstly,":[15],"the":[16,30,42,47,52,72,82,91,102,108,118],"existence,":[17],"multiplicity,":[18],"patterns":[20],"of":[21,36,44,46,86,94,104,121,124],"spatially":[22,57],"nonhomogeneous":[23,58],"steady-state":[24,60,75],"solution":[25,76],"are":[26],"obtained":[27],"by":[28,34],"using":[29,81],"Lyapunov\u2013Schmidt":[31],"reduction.":[32],"Secondly,":[33],"means":[35],"space":[37],"decomposition,":[38],"we":[39,64,98],"subtly":[40],"discuss":[41],"distribution":[43],"eigenvalues":[45],"infinitesimal":[48],"generator":[49],"associated":[50],"linearized":[53],"system":[54],"at":[55],"synchronous":[59,74],"solution,":[61],"then":[63],"derive":[65],"some":[66,114],"sufficient":[67],"conditions":[68],"to":[69],"ensure":[70],"that":[71],"nontrivial":[73],"asymptotically":[78],"stable.":[79],"By":[80],"symmetric":[83],"bifurcation":[84,120],"theory":[85,93],"differential":[87],"equations":[88],"together":[89],"representation":[92],"standard":[95],"dihedral":[96],"groups,":[97],"not":[99],"only":[100],"investigate":[101],"time":[105],"on":[107,117],"pattern":[109],"formation,":[110],"but":[111],"also":[112],"obtain":[113],"important":[115],"results":[116],"spontaneous":[119],"multiple":[122],"branches":[123],"nonlinear":[125],"wave":[126],"solutions":[127],"their":[129],"spatiotemporal":[130],"patterns.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}