{"id":"https://openalex.org/W4385639780","doi":"https://doi.org/10.1142/s021812742350102x","title":"Bifurcation Analysis and Steady-State Patterns in Reaction\u2013Diffusion Systems Augmented with Self- and Cross-Diffusion","display_name":"Bifurcation Analysis and Steady-State Patterns in Reaction\u2013Diffusion Systems Augmented with Self- and Cross-Diffusion","publication_year":2023,"publication_date":"2023-07-01","ids":{"openalex":"https://openalex.org/W4385639780","doi":"https://doi.org/10.1142/s021812742350102x"},"language":"en","primary_location":{"id":"doi:10.1142/s021812742350102x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742350102x","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/A5062802365","display_name":"Benjamin Aymard","orcid":"https://orcid.org/0000-0003-1094-0373"},"institutions":[{"id":"https://openalex.org/I4210106545","display_name":"Centre Inria d'Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106545"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Benjamin Aymard","raw_affiliation_strings":["MathNeuro Team, Inria Sophia Antipolis M\u00e9diterran\u00e9e, Sophia Antipolis Cedex, France"],"raw_orcid":"https://orcid.org/0000-0003-1094-0373","affiliations":[{"raw_affiliation_string":"MathNeuro Team, Inria Sophia Antipolis M\u00e9diterran\u00e9e, Sophia Antipolis Cedex, France","institution_ids":["https://openalex.org/I4210106545"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062802365"],"corresponding_institution_ids":["https://openalex.org/I4210106545"],"apc_list":null,"apc_paid":null,"fwci":0.5903,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68254106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"33","issue":"09","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/nonlinear-system","display_name":"Nonlinear system","score":0.6409464478492737},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5679887533187866},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4956015348434448},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4874468147754669},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.487080842256546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4856773614883423},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4801042377948761},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.46435049176216125},{"id":"https://openalex.org/keywords/dependency","display_name":"Dependency (UML)","score":0.42379266023635864},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.4166719317436218},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38957148790359497},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34683895111083984},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3415059447288513},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2715868055820465},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.201869934797287},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.08466991782188416},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07610493898391724}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6409464478492737},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5679887533187866},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4956015348434448},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4874468147754669},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.487080842256546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4856773614883423},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4801042377948761},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46435049176216125},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.42379266023635864},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.4166719317436218},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38957148790359497},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34683895111083984},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3415059447288513},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2715868055820465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.201869934797287},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08466991782188416},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07610493898391724},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","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/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/s021812742350102x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742350102x","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":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1938657618","https://openalex.org/W1973118029","https://openalex.org/W1980661496","https://openalex.org/W2006640177","https://openalex.org/W2024748736","https://openalex.org/W2064341276","https://openalex.org/W2082187902","https://openalex.org/W2082395037","https://openalex.org/W2092424552","https://openalex.org/W2093708215","https://openalex.org/W2117450472","https://openalex.org/W2169791857","https://openalex.org/W2193955221","https://openalex.org/W2315259430","https://openalex.org/W2810126555","https://openalex.org/W3143360112","https://openalex.org/W3210248416","https://openalex.org/W4206651839","https://openalex.org/W4206691827","https://openalex.org/W4237669967","https://openalex.org/W4238329465","https://openalex.org/W4293150024","https://openalex.org/W4388311457"],"related_works":["https://openalex.org/W2067317451","https://openalex.org/W4211085505","https://openalex.org/W2154771632","https://openalex.org/W2084758217","https://openalex.org/W3122478268","https://openalex.org/W408804804","https://openalex.org/W2743679792","https://openalex.org/W2363489175","https://openalex.org/W2389421446","https://openalex.org/W2024551343"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"a":[3,24,63,138,151],"study":[4],"of":[5,8,40,50,81,140,147,156],"long-term":[6],"behavior":[7],"reaction\u2013diffusion":[9],"systems":[10],"augmented":[11,20],"with":[12,55,130,143],"self-":[13],"and":[14,31,85,102,150],"cross-diffusion":[15],"is":[16,32,68,96,115,121],"reported,":[17],"using":[18,93,103],"an":[19],"Gray\u2013Scott":[21],"system":[22],"as":[23],"generic":[25],"example.":[26],"The":[27],"methodology":[28],"remains":[29],"general,":[30],"therefore":[33],"applicable":[34],"to":[35,72],"some":[36],"other":[37],"systems.":[38],"Simulations":[39],"the":[41,48,75,82,110,112,141,144,148,154,157],"temporal":[42,83],"model":[43],"(nonlinear":[44,78],"parabolic":[45],"system)":[46,80],"reveal":[47],"presence":[49],"steady":[51,76],"states,":[52],"often":[53],"associated":[54],"energy":[56],"dissipation.":[57],"A":[58,118],"Newton":[59],"method":[60,67],"based":[61],"on":[62,153],"mixed":[64],"finite":[65],"element":[66],"provided,":[69],"in":[70],"order":[71],"directly":[73],"evaluate":[74],"states":[77],"elliptic":[79],"system,":[84,149],"validated":[86],"against":[87],"its":[88],"solutions.":[89],"Linear":[90],"stability":[91],"analysis":[92,95,105],"Fourier":[94],"carried":[97],"out":[98],"around":[99,106],"homogeneous":[100],"equilibrium,":[101],"spectral":[104,113],"nonhomogeneous":[107],"ones.":[108],"For":[109],"latter,":[111],"problem":[114],"solved":[116],"numerically.":[117],"multiparameter":[119],"bifurcation":[120],"reported.":[122],"Original":[123],"steady-state":[124],"patterns":[125],"are":[126],"unveiled,":[127],"not":[128],"observable":[129],"linear":[131],"diffusion":[132],"only.":[133],"Two":[134],"key":[135],"observations":[136],"are:":[137],"dependency":[139,152],"pattern":[142],"initial":[145],"condition":[146],"geometry":[155],"domain.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
