{"id":"https://openalex.org/W1995162135","doi":"https://doi.org/10.1137/130949798","title":"Nonlinear Stability through Algebraically Decaying Point Spectrum: Applications to Nonlocal Interaction Equations","display_name":"Nonlinear Stability through Algebraically Decaying Point Spectrum: Applications to Nonlocal Interaction Equations","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1995162135","doi":"https://doi.org/10.1137/130949798","mag":"1995162135"},"language":"en","primary_location":{"id":"doi:10.1137/130949798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130949798","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/A5003036990","display_name":"James H. von Brecht","orcid":null},"institutions":[{"id":"https://openalex.org/I59897056","display_name":"California State University, Long Beach","ror":"https://ror.org/0080fxk18","country_code":"US","type":"education","lineage":["https://openalex.org/I59897056"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James H. von Brecht","raw_affiliation_strings":["California State University-Long Beach"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California State University-Long Beach","institution_ids":["https://openalex.org/I59897056"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003184921","display_name":"Scott G. McCalla","orcid":"https://orcid.org/0000-0003-0093-4658"},"institutions":[{"id":"https://openalex.org/I23732399","display_name":"Montana State University","ror":"https://ror.org/02w0trx84","country_code":"US","type":"education","lineage":["https://openalex.org/I23732399","https://openalex.org/I4210126032"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott G. McCalla","raw_affiliation_strings":["Montana State Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Montana State Univ","institution_ids":["https://openalex.org/I23732399"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6971,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69653475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"46","issue":"6","first_page":"3727","last_page":"3760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9987999796867371,"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":0.9987000226974487,"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/mathematics","display_name":"Mathematics","score":0.8587092161178589},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7727314233779907},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.6929681301116943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6017338633537292},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5431593060493469},{"id":"https://openalex.org/keywords/essential-spectrum","display_name":"Essential spectrum","score":0.5157456994056702},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.5105822682380676},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4906853437423706},{"id":"https://openalex.org/keywords/linear-stability","display_name":"Linear stability","score":0.46561217308044434},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4218962788581848},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.41169029474258423},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3570292294025421},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25352317094802856},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1339183747768402},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1022476851940155}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8587092161178589},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7727314233779907},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.6929681301116943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6017338633537292},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5431593060493469},{"id":"https://openalex.org/C2780297109","wikidata":"https://www.wikidata.org/wiki/Q917390","display_name":"Essential spectrum","level":3,"score":0.5157456994056702},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5105822682380676},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4906853437423706},{"id":"https://openalex.org/C43466630","wikidata":"https://www.wikidata.org/wiki/Q17098945","display_name":"Linear stability","level":3,"score":0.46561217308044434},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4218962788581848},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.41169029474258423},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3570292294025421},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25352317094802856},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1339183747768402},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1022476851940155},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130949798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130949798","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W141185090","https://openalex.org/W163224475","https://openalex.org/W1560060148","https://openalex.org/W1621484501","https://openalex.org/W1867357266","https://openalex.org/W1964272822","https://openalex.org/W1964310342","https://openalex.org/W1968130967","https://openalex.org/W1970255730","https://openalex.org/W1986641297","https://openalex.org/W1999040016","https://openalex.org/W1999577479","https://openalex.org/W1999665628","https://openalex.org/W2003297161","https://openalex.org/W2006078471","https://openalex.org/W2006907269","https://openalex.org/W2008702562","https://openalex.org/W2012205310","https://openalex.org/W2024135455","https://openalex.org/W2030193783","https://openalex.org/W2031064936","https://openalex.org/W2034865749","https://openalex.org/W2035731630","https://openalex.org/W2038322642","https://openalex.org/W2040416019","https://openalex.org/W2041440299","https://openalex.org/W2042564923","https://openalex.org/W2045899820","https://openalex.org/W2049817674","https://openalex.org/W2052946502","https://openalex.org/W2054113155","https://openalex.org/W2054821686","https://openalex.org/W2055515432","https://openalex.org/W2059999403","https://openalex.org/W2060699702","https://openalex.org/W2061905804","https://openalex.org/W2067711323","https://openalex.org/W2077366558","https://openalex.org/W2083765731","https://openalex.org/W2086996241","https://openalex.org/W2087796497","https://openalex.org/W2102228124","https://openalex.org/W2112543799","https://openalex.org/W2119323323","https://openalex.org/W2119414533","https://openalex.org/W2126564632","https://openalex.org/W2134246159","https://openalex.org/W2139431382","https://openalex.org/W2149165239","https://openalex.org/W2155385278","https://openalex.org/W2156934943","https://openalex.org/W2157942701","https://openalex.org/W2168688381","https://openalex.org/W2335366936","https://openalex.org/W2461150107","https://openalex.org/W2949342685","https://openalex.org/W3047703851","https://openalex.org/W3100014801","https://openalex.org/W3104332327","https://openalex.org/W3104386349"],"related_works":["https://openalex.org/W2347535072","https://openalex.org/W2952745759","https://openalex.org/W1968201932","https://openalex.org/W2349083538","https://openalex.org/W2165516351","https://openalex.org/W2183595797","https://openalex.org/W2008373210","https://openalex.org/W3139302145","https://openalex.org/W2754787911","https://openalex.org/W1540542550"],"abstract_inverted_index":{"Nonlocal":[0],"interaction":[1],"equations,":[2],"such":[3,77],"as":[4],"aggregation":[5],"equations":[6],"and":[7,59],"a":[8],"number":[9],"of":[10,25,34,76],"related":[11],"models":[12],"for":[13],"biological":[14],"swarming,":[15],"can":[16],"exhibit":[17],"compact,":[18],"co-dimension":[19],"one":[20],"equilibrium":[21],"solutions.":[22],"Nonlinear":[23],"stability":[24,66,72],"these":[26],"solutions":[27],"crucially":[28],"depends":[29],"on":[30,43],"understanding":[31],"the":[32,44,54,57,60,74,97],"properties":[33],"operators":[35],"whose":[36],"linearizations":[37],"have":[38],"point":[39,80],"spectrum":[40],"that":[41],"accumulates":[42],"imaginary":[45],"axis.":[46],"In":[47],"this":[48],"paper,":[49],"we":[50],"establish":[51],"criteria":[52],"upon":[53],"linear":[55,65],"operator,":[56],"nonlinearity,":[58],"admissible":[61,89],"perturbations":[62,90],"under":[63],"which":[64,88],"is":[67],"sufficient":[68],"to":[69,92,99],"guarantee":[70],"nonlinear":[71],"in":[73],"presence":[75],"algebraically":[78],"decaying":[79],"spectrum.":[81],"We":[82,94],"also":[83],"provide":[84],"temporal":[85],"rates":[86],"at":[87],"decay":[91],"zero.":[93],"then":[95],"apply":[96],"theory":[98],"some":[100],"simplified":[101],"nonlocal":[102],"equations.":[103]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
