{"id":"https://openalex.org/W2765856888","doi":"https://doi.org/10.1137/16m1097560","title":"Spatiotemporal Dynamics of the Diffusive Mussel-Algae Model Near Turing-Hopf Bifurcation","display_name":"Spatiotemporal Dynamics of the Diffusive Mussel-Algae Model Near Turing-Hopf Bifurcation","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2765856888","doi":"https://doi.org/10.1137/16m1097560","mag":"2765856888"},"language":"en","primary_location":{"id":"doi:10.1137/16m1097560","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1097560","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","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/A5026187828","display_name":"Yongli Song","orcid":"https://orcid.org/0000-0002-2209-2458"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yongli Song","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089559378","display_name":"Heping Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heping Jiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027488634","display_name":"Quan\u2010Xing Liu","orcid":"https://orcid.org/0000-0002-8602-0154"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Quan-Xing Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100334757","display_name":"Yuan Yuan","orcid":"https://orcid.org/0000-0002-3601-5322"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuan Yuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026187828"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.5912,"has_fulltext":false,"cited_by_count":122,"citation_normalized_percentile":{"value":0.98396496,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"16","issue":"4","first_page":"2030","last_page":"2062"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9959999918937683,"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":0.9883999824523926,"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":0.7249579429626465},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.5642642378807068},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5118011832237244},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5091070532798767},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.4814681112766266},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.47939229011535645},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4481121003627777},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.4353589713573456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43501999974250793},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"Pattern formation","score":0.4212639629840851},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40621015429496765},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38932478427886963},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24634897708892822},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1509576141834259}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7249579429626465},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.5642642378807068},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5118011832237244},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5091070532798767},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.4814681112766266},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47939229011535645},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4481121003627777},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.4353589713573456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43501999974250793},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.4212639629840851},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40621015429496765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38932478427886963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24634897708892822},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1509576141834259},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","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/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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1097560","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1097560","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/14","display_name":"Life below water","score":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G7076157404","display_name":null,"funder_award_id":"41676084","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8940736242","display_name":null,"funder_award_id":"11571257","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W211828493","https://openalex.org/W797100396","https://openalex.org/W1822833310","https://openalex.org/W1929947366","https://openalex.org/W1972115738","https://openalex.org/W1975687915","https://openalex.org/W1976180149","https://openalex.org/W1977031359","https://openalex.org/W1980661496","https://openalex.org/W1987631246","https://openalex.org/W1987984915","https://openalex.org/W1990042727","https://openalex.org/W1990167663","https://openalex.org/W1992171048","https://openalex.org/W1993999944","https://openalex.org/W1995043208","https://openalex.org/W1995998068","https://openalex.org/W1997748595","https://openalex.org/W2006191040","https://openalex.org/W2009354787","https://openalex.org/W2014564062","https://openalex.org/W2015751185","https://openalex.org/W2032721893","https://openalex.org/W2036423516","https://openalex.org/W2038105662","https://openalex.org/W2039005786","https://openalex.org/W2046181545","https://openalex.org/W2046573764","https://openalex.org/W2047506587","https://openalex.org/W2049852697","https://openalex.org/W2073644145","https://openalex.org/W2074603814","https://openalex.org/W2084702778","https://openalex.org/W2086126894","https://openalex.org/W2086222060","https://openalex.org/W2090347294","https://openalex.org/W2091480729","https://openalex.org/W2092619359","https://openalex.org/W2095718501","https://openalex.org/W2098347389","https://openalex.org/W2100530733","https://openalex.org/W2101173516","https://openalex.org/W2102124893","https://openalex.org/W2102265921","https://openalex.org/W2105801075","https://openalex.org/W2111805068","https://openalex.org/W2120330615","https://openalex.org/W2134279070","https://openalex.org/W2138634725","https://openalex.org/W2153268540","https://openalex.org/W2160613953","https://openalex.org/W2169045269","https://openalex.org/W2469442700","https://openalex.org/W2479322662"],"related_works":["https://openalex.org/W1987790493","https://openalex.org/W2153388945","https://openalex.org/W2038701038","https://openalex.org/W1975783007","https://openalex.org/W2382752082","https://openalex.org/W1988489950","https://openalex.org/W4312255936","https://openalex.org/W4313700716","https://openalex.org/W1986426368","https://openalex.org/W2363522146"],"abstract_inverted_index":{"Intertidal":[0],"mussels":[1],"can":[2],"self-organize":[3],"into":[4],"periodic":[5],"spot,":[6],"stripe,":[7],"labyrinth,":[8],"and":[9,29,61,66,85,96,107,124],"gap":[10],"patterns":[11,123],"ranging":[12],"from":[13],"centimeter":[14],"to":[15],"meter":[16],"scales.":[17],"The":[18,53],"leading":[19],"mathematical":[20],"explanations":[21],"for":[22,129],"these":[23],"phenomena":[24],"are":[25,69],"the":[26,30,37,43,49,56,62,73,81,87,98,102,119,126,130],"reaction-diffusion-advection":[27],"model":[28],"phase":[31],"separation":[32],"model.":[33,52],"This":[34],"paper":[35],"continues":[36],"series":[38],"studies":[39],"on":[40,80,101],"analytically":[41],"understanding":[42],"existence":[44,63],"of":[45,55,64,121],"pattern":[46,131],"solutions":[47],"in":[48,91],"reaction-diffusion":[50],"mussel-algae":[51],"stability":[54],"positive":[57],"constant":[58],"steady":[59],"state":[60],"Hopf":[65],"steady-state":[67],"bifurcations":[68],"studied":[70],"by":[71,94],"analyzing":[72],"corresponding":[74],"characteristic":[75],"equation.":[76],"Furthermore,":[77],"we":[78,110],"focus":[79],"Turing-Hopf":[82],"(TH)":[83],"bifurcation":[84],"obtain":[86],"explicit":[88],"dynamical":[89],"classification":[90],"its":[92],"neighborhood":[93],"calculating":[95],"investigating":[97],"normal":[99],"form":[100],"center":[103],"manifold.":[104],"Using":[105],"theoretical":[106],"numerical":[108],"simulations,":[109],"demonstrates":[111],"that":[112],"this":[113],"TH":[114],"interaction":[115],"would":[116],"significantly":[117],"enhance":[118],"diversity":[120],"spatial":[122],"trigger":[125],"alternative":[127],"paths":[128],"development.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":22},{"year":2018,"cited_by_count":11}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
