{"id":"https://openalex.org/W2796509392","doi":"https://doi.org/10.1137/17m1127594","title":"Spectra and Stability of Spatially Periodic Pulse Patterns II: The Critical Spectral Curve","display_name":"Spectra and Stability of Spatially Periodic Pulse Patterns II: The Critical Spectral Curve","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2796509392","doi":"https://doi.org/10.1137/17m1127594","mag":"2796509392"},"language":"en","primary_location":{"id":"doi:10.1137/17m1127594","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1127594","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5037989662","display_name":"Bj\u00f6rn de Rijk","orcid":"https://orcid.org/0000-0003-0390-274X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bj\u00f6rn de Rijk","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037989662"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7381,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.7359656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"2","first_page":"1958","last_page":"2019"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8103370666503906},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.6438818573951721},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.6267269849777222},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5862653851509094},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5413612723350525},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5194620490074158},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.47275835275650024},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4612084925174713},{"id":"https://openalex.org/keywords/spectral-theory","display_name":"Spectral theory","score":0.42922142148017883},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.1600247323513031},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13392004370689392}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8103370666503906},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6438818573951721},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.6267269849777222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5862653851509094},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5413612723350525},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5194620490074158},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.47275835275650024},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4612084925174713},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.42922142148017883},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.1600247323513031},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13392004370689392},{"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/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1127594","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1127594","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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":44,"referenced_works":["https://openalex.org/W141185090","https://openalex.org/W183319324","https://openalex.org/W1487057719","https://openalex.org/W1533288419","https://openalex.org/W1540580484","https://openalex.org/W1560060148","https://openalex.org/W1608637423","https://openalex.org/W1834990783","https://openalex.org/W1967724962","https://openalex.org/W1969154522","https://openalex.org/W1985940938","https://openalex.org/W1986364663","https://openalex.org/W1986557898","https://openalex.org/W1989095982","https://openalex.org/W1989248529","https://openalex.org/W1991274168","https://openalex.org/W2016767879","https://openalex.org/W2019177912","https://openalex.org/W2040298259","https://openalex.org/W2040718349","https://openalex.org/W2040995216","https://openalex.org/W2044772350","https://openalex.org/W2053733537","https://openalex.org/W2059988646","https://openalex.org/W2070823330","https://openalex.org/W2077996415","https://openalex.org/W2080122981","https://openalex.org/W2082741679","https://openalex.org/W2088754516","https://openalex.org/W2092999826","https://openalex.org/W2106465020","https://openalex.org/W2115750337","https://openalex.org/W2119520813","https://openalex.org/W2122013064","https://openalex.org/W2127341386","https://openalex.org/W2141061348","https://openalex.org/W2146004828","https://openalex.org/W2162155774","https://openalex.org/W2279446551","https://openalex.org/W2404712178","https://openalex.org/W2419464796","https://openalex.org/W2810917376","https://openalex.org/W2963247128","https://openalex.org/W3102799673"],"related_works":["https://openalex.org/W2363992932","https://openalex.org/W2066340280","https://openalex.org/W1999123830","https://openalex.org/W2971991931","https://openalex.org/W2054807178","https://openalex.org/W2043723919","https://openalex.org/W2623381607","https://openalex.org/W4200274144","https://openalex.org/W2028231540","https://openalex.org/W3031650250"],"abstract_inverted_index":{"In":[0,215],"the":[1,12,27,30,33,45,48,62,75,80,120,130,150,155,158,171,175,178,194,221,229,235,278],"stability":[2,254],"analysis":[3],"of":[4,29,70,101,146,267],"pulse":[5,110],"patterns":[6,136],"in":[7,47,57,95,137,157,177,193,263],"singularly":[8],"perturbed":[9],"reaction-diffusion":[10,102,271],"systems,":[11],"scale":[13],"separation":[14],"is":[15,112,143,181],"often":[16],"exploited":[17],"to":[18,25,92,108,115,125,149,154,183,234],"reduce":[19],"complexity.":[20],"There":[21],"are":[22,69,82],"various":[23],"methods":[24,53,89,122],"decompose":[26],"spectrum":[28,46,147,176],"linearization":[31],"about":[32],"pattern":[34],"into":[35,277],"slow":[36,76],"and":[37,40,65,202,243,255],"fast":[38],"pieces":[39],"thus":[41],"gain":[42,275],"control":[43,128,227],"over":[44,228],"asymptotic":[49,126,159,179],"limit.":[50],"These":[51],"reduction":[52,121],"have":[54],"been":[55,191],"developed":[56],"prototype":[58],"models":[59],"such":[60],"as":[61],"FitzHugh--Nagumo,":[63],"Gray--Scott,":[64],"Gierer--Meinhardt":[66],"equations,":[67],"which":[68],"slowly":[71,98,138,269],"linear":[72,85],"nature;":[73],"i.e.,":[74],"dynamics":[77],"away":[78],"from":[79],"pulses":[81,94,132,164,262],"driven":[83],"by":[84],"equations.":[86],"Recently,":[87],"these":[88],"were":[90],"extended":[91],"homoclinic":[93,131,163],"a":[96,105,144,166,264],"general,":[97],"nonlinear":[99,139,253],"class":[100,266],"systems.":[103,140,272],"Yet,":[104],"straightforward":[106],"extension":[107],"periodic":[109,135,261],"solutions":[111],"impossible":[113],"due":[114],"two":[116],"major":[117],"obstructions.":[118],"First,":[119],"that":[123,152],"lead":[124],"spectral":[127,231],"for":[129,134,162,252,257],"fail":[133],"Second,":[141],"there":[142],"curve":[145,232],"attached":[148,233],"origin":[151,156],"shrinks":[153],"limit,":[160],"whereas":[161],"only":[165],"simple":[167],"eigenvalue":[168],"resides":[169],"at":[170],"origin.":[172,236],"Therefore,":[173],"controlling":[174],"limit":[180],"insufficient":[182],"decide":[184],"upon":[185],"stability.":[186],"The":[187,237],"first":[188],"obstruction":[189],"has":[190],"addressed":[192],"companion":[195],"paper":[196,217],"[B.":[197],"de":[198],"Rijk,":[199],"A.":[200],"Doelman,":[201],"J.":[203,208],"D.":[204],"M.":[205],"Rademacher,":[206],"SIAM":[207],"Math.":[209],"Anal.,":[210],"48":[211],"(2016),":[212],"pp.":[213],"61--121].":[214],"this":[216],"we":[218,224,274],"focus":[219],"on":[220,240],"second":[222],"obstruction:":[223],"obtain":[225],"leading-order":[226],"critical":[230],"proof":[238],"relies":[239],"Lin's":[241],"method":[242],"utilizes":[244],"exponential":[245],"trichotomies.":[246],"Our":[247],"results":[248],"yield":[249],"explicit":[250],"conditions":[251],"instability":[256],"stationary,":[258],"spatially":[259],"symmetric,":[260],"large":[265],"multicomponent,":[268],"nonlinear,":[270],"Moreover,":[273],"insight":[276],"associated":[279],"destabilization":[280],"mechanisms.":[281]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}