{"id":"https://openalex.org/W1985314283","doi":"https://doi.org/10.1137/s0036139998349298","title":"Wave-Block in Excitable Media Due to Regions of Depressed Excitability","display_name":"Wave-Block in Excitable Media Due to Regions of Depressed Excitability","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1985314283","doi":"https://doi.org/10.1137/s0036139998349298","mag":"1985314283"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139998349298","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139998349298","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/A5071828704","display_name":"James P. Keener","orcid":"https://orcid.org/0000-0001-9216-4157"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James P. Keener","raw_affiliation_strings":["New York University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103223176","display_name":"Timothy J. Lewis","orcid":"https://orcid.org/0000-0003-1885-746X"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy J. Lewis","raw_affiliation_strings":["New York University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I57206974"],"apc_list":null,"apc_paid":null,"fwci":4.7796,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.94864557,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"61","issue":"1","first_page":"293","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":1.0,"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":1.0,"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":0.9987999796867371,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9972000122070312,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bistability","display_name":"Bistability","score":0.749970555305481},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7260422110557556},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6364830732345581},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6194788813591003},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.5733527541160583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5677824020385742},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5656378269195557},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5470987558364868},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.47910788655281067},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47789061069488525},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33567148447036743},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22843390703201294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18713337182998657},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1685861051082611},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13122430443763733}],"concepts":[{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.749970555305481},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7260422110557556},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6364830732345581},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6194788813591003},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.5733527541160583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5677824020385742},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5656378269195557},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5470987558364868},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.47910788655281067},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47789061069488525},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33567148447036743},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22843390703201294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18713337182998657},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1685861051082611},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13122430443763733},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/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:10.1137/s0036139998349298","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139998349298","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W43144976","https://openalex.org/W1510003436","https://openalex.org/W1518428823","https://openalex.org/W1969182281","https://openalex.org/W1984336411","https://openalex.org/W1984535955","https://openalex.org/W1985875536","https://openalex.org/W1985940938","https://openalex.org/W1992987522","https://openalex.org/W1993693726","https://openalex.org/W1999930428","https://openalex.org/W2007910408","https://openalex.org/W2008430715","https://openalex.org/W2011021720","https://openalex.org/W2020718248","https://openalex.org/W2022748003","https://openalex.org/W2033923794","https://openalex.org/W2046904024","https://openalex.org/W2051749323","https://openalex.org/W2055826414","https://openalex.org/W2058858982","https://openalex.org/W2065799397","https://openalex.org/W2067265108","https://openalex.org/W2068597145","https://openalex.org/W2074907137","https://openalex.org/W2075016205","https://openalex.org/W2077243741","https://openalex.org/W2079949023","https://openalex.org/W2084791325","https://openalex.org/W2085949935","https://openalex.org/W2086169207","https://openalex.org/W2088080912","https://openalex.org/W2114642178","https://openalex.org/W2207223089","https://openalex.org/W2283807792","https://openalex.org/W2498110550","https://openalex.org/W2577663557","https://openalex.org/W4255489875"],"related_works":["https://openalex.org/W3103578537","https://openalex.org/W189436430","https://openalex.org/W2094377213","https://openalex.org/W4312533727","https://openalex.org/W2051512300","https://openalex.org/W2038734117","https://openalex.org/W2356828619","https://openalex.org/W2068526439","https://openalex.org/W2074466359","https://openalex.org/W2091792699"],"abstract_inverted_index":{"We":[0,43,117],"study":[1],"propagation":[2,105],"failure":[3],"using":[4],"the":[5,24,37,54,75,80,83,86,96,99,102],"one-dimensional":[6],"scalar":[7],"bistable":[8],"equation":[9],"with":[10,125,132],"a":[11,45,60,133],"passive":[12],"\"gap\"":[13],"region.":[14],"By":[15],"applying":[16],"comparison":[17],"principles":[18],"for":[19,29,36],"this":[20],"type":[21],"of":[22,26,39,79,85,101],"equation,":[23],"problem":[25,81],"finding":[27,34],"conditions":[28,35],"block":[30,123],"is":[31],"reduced":[32],"to":[33,51,73,113,120],"existence":[38],"steady":[40,61,87],"state":[41,62,88],"solutions.":[42,89],"present":[44],"geometrical":[46],"method":[47,70,108],"that":[48,122],"allows":[49],"one":[50],"easily":[52,110],"compute":[53],"critical":[55],"gap":[56,115],"length":[57],"above":[58],"which":[59],"solution,":[63],"and":[64,104],"thus":[65],"block,":[66],"first":[67],"occurs.":[68],"The":[69,107],"also":[71],"helps":[72],"uncover":[74],"general":[76],"bifurcation":[77],"structure":[78],"including":[82],"stability":[84],"In":[90],"obtaining":[91],"these":[92],"results,":[93],"we":[94],"characterize":[95],"relationship":[97],"between":[98],"properties":[100],"system":[103],"failure.":[106],"can":[109],"be":[111,130],"extended":[112],"other":[114],"dynamics.":[116],"use":[118],"it":[119],"show":[121],"associated":[124,131],"any":[126],"local":[127],"inhomogeneity":[128],"must":[129],"limit":[134],"point":[135],"bifurcation.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
