{"id":"https://openalex.org/W2084302413","doi":"https://doi.org/10.1137/s0036139998344635","title":"A Reaction-Diffusion System with Periodic Front Dynamics","display_name":"A Reaction-Diffusion System with Periodic Front Dynamics","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2084302413","doi":"https://doi.org/10.1137/s0036139998344635","mag":"2084302413"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139998344635","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139998344635","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","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/A5071873811","display_name":"Georgiy S. Medvedev","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Georgiy S. Medvedev","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077516931","display_name":"Nancy Kopell","orcid":"https://orcid.org/0000-0002-8568-8750"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nancy Kopell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5087776335","display_name":"Tasso J. Kaper","orcid":"https://orcid.org/0000-0003-0028-6865"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tasso J. Kaper","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071873811"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.1487743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"60","issue":"5","first_page":"1601","last_page":"1638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9901999831199646,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.6731194853782654},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.574943482875824},{"id":"https://openalex.org/keywords/front","display_name":"Front (military)","score":0.5667029023170471},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5123430490493774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4740317165851593},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40412503480911255},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3929736316204071},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3529791831970215},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3238493800163269},{"id":"https://openalex.org/keywords/meteorology","display_name":"Meteorology","score":0.1266232430934906},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.12200984358787537}],"concepts":[{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.6731194853782654},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.574943482875824},{"id":"https://openalex.org/C2777551076","wikidata":"https://www.wikidata.org/wiki/Q842332","display_name":"Front (military)","level":2,"score":0.5667029023170471},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5123430490493774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4740317165851593},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40412503480911255},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3929736316204071},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3529791831970215},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3238493800163269},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.1266232430934906},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.12200984358787537},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139998344635","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139998344635","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.70.7","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.7","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wolff.bu.edu/publ/local/GMedvedevTKaperandNKopell_Areactiondiffusionsystemwithperiodicfrontdynamics_SIAMJApplMath_60_16011638.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.5299999713897705,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W140547310","https://openalex.org/W561377653","https://openalex.org/W1532777065","https://openalex.org/W1550382162","https://openalex.org/W1583602735","https://openalex.org/W1602967628","https://openalex.org/W1788856903","https://openalex.org/W1970868143","https://openalex.org/W1971582676","https://openalex.org/W1979893394","https://openalex.org/W1982540504","https://openalex.org/W1987139950","https://openalex.org/W2015892872","https://openalex.org/W2034828918","https://openalex.org/W2038991247","https://openalex.org/W2042892258","https://openalex.org/W2048615939","https://openalex.org/W2048915347","https://openalex.org/W2062452180","https://openalex.org/W2071966541","https://openalex.org/W2083491866","https://openalex.org/W2085153899","https://openalex.org/W2087141207","https://openalex.org/W2130370541","https://openalex.org/W2167929682","https://openalex.org/W2369386221","https://openalex.org/W2487775498","https://openalex.org/W2574013312","https://openalex.org/W2914452696","https://openalex.org/W2967819933"],"related_works":["https://openalex.org/W4210368779","https://openalex.org/W4232652765","https://openalex.org/W1416210464","https://openalex.org/W1520404809","https://openalex.org/W2382549550","https://openalex.org/W2164612159","https://openalex.org/W2951555841","https://openalex.org/W2006635773","https://openalex.org/W4238727794","https://openalex.org/W1481030933"],"abstract_inverted_index":{"A":[0],"reaction-diffusion":[1],"model":[2,44,89],"motivated":[3],"by":[4],"Proteus":[5,38],"mirabilis":[6,39],"swarm":[7,24,62,73,127,165,178],"colony":[8,92,124,158,171,246,283],"development":[9],"is":[10,69,301],"presented":[11],"and":[12,26,32,47,59,106,146,148,166,190,210,213,224,252,290,323,361,370],"analyzed":[13],"in":[14,86,94,117,161,243,253,288,349,365],"this":[15,142,303],"work.":[16],"The":[17,41,88],"principal":[18],"variables":[19],"are":[20,30,111],"the":[21,37,45,51,57,72,82,120,123,137,150,157,164,170,177,185,191,197,208,218,234,237,245,249,254,261,270,279,282,297,310,319,324,328,338,341,344,359,366],"concentrations":[22,168,339],"of":[23,36,50,61,81,99,202,220,236,256,309,318,343,374],"cells":[25,128],"swimmer":[27,52,167],"cells,":[28,53],"which":[29,95,155],"multicellular":[31],"single-cell":[33],"forms,":[34],"respectively,":[35],"bacteria.":[40],"kinetic":[42],"terms":[43],"growth":[46],"division":[48],"process":[49],"as":[54,56,126,205,207],"well":[55,206],"formation":[58],"septation":[60],"cells.":[63],"In":[64,265],"addition,":[65],"a":[66,103,107,133,183,240,274,292,350],"nonlinear":[67],"diffusion":[68],"employed":[70],"for":[71,226,358,371],"cell":[74,179],"migration":[75],"that":[76,233,269,276,305,331,337],"incorporates":[77],"several":[78],"essential":[79],"aspects":[80],"concentration-dependent":[83],"dynamics":[84,235,312,322],"observed":[85],"experiments.":[87,118],"exhibits":[90],"time-periodic":[91,351],"evolution":[93,247],"each":[96],"period":[97],"consists":[98],"two":[100,345],"distinct":[101],"phases:":[102],"swarming":[104,121,193,263,320],"phase":[105,152,187,194,251,321,330],"consolidation":[108,151,186,250,329],"phase.":[109,264],"Both":[110],"very":[112],"similar":[113],"to":[114,131,260,315,327],"those":[115],"seen":[116],"During":[119],"phase,":[122],"expands":[125],"migrate":[129],"outward":[130],"form":[132],"new":[134],"terrace":[135],"beyond":[136],"colony's":[138],"initial":[139],"boundary.":[140,284,298],"Gradually,":[141],"expansion":[143],"slows":[144],"down":[145],"stops,":[147],"then":[149],"begins,":[153,195],"during":[154,248],"time":[156],"boundary":[159,172],"stays":[160],"place,":[162],"but":[163],"inside":[169],"change":[173],"significantly.":[174],"Finally,":[175,353],"when":[176,294],"concentration":[180],"has":[181],"reached":[182],"threshold,":[184],"ends":[188],"abruptly":[189],"next":[192],"repeating":[196],"cycle.":[198],"We":[199,231],"analyze":[200],"both":[201],"these":[203],"phases,":[204],"transitions":[209],"switches":[211],"(gradual":[212],"abrupt)":[214],"between":[215],"them,":[216],"using":[217],"method":[219],"matched":[221,367],"asymptotic":[222,368],"expansions":[223],"theory":[225],"parabolic":[227],"partial":[228],"differential":[229],"equations.":[230],"show":[232,268,336],"diffusivity":[238,271,311],"play":[239],"central":[241],"role":[242],"determining":[244],"occurrence":[255],"an":[257,316],"abrupt":[258],"transition":[259,326],"subsequent":[262],"particular,":[266],"we":[267,354],"profile":[272],"forms":[273,291],"wave":[275],"propagates":[277],"behind":[278],"front":[280],"toward":[281],"It":[285],"grows":[286],"sharply":[287],"amplitude":[289],"spike":[293],"it":[295,300],"reaches":[296],"Moreover,":[299],"precisely":[302],"event":[304],"triggers":[306],"swarming.":[307],"Analysis":[308],"also":[313],"leads":[314],"understanding":[317],"gradual":[325],"follows":[332],"it.":[333],"These":[334],"analyses":[335],"at":[340],"beginning":[342],"phases":[346],"naturally":[347],"repeat":[348],"manner.":[352],"present":[355],"rigorous":[356],"estimates":[357],"inner":[360],"outer":[362],"solutions":[363],"developed":[364],"analysis,":[369],"their":[372],"domains":[373],"validity.":[375]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}