{"id":"https://openalex.org/W1994762657","doi":"https://doi.org/10.1137/06066638x","title":"Patterns and Features of Families of Traveling Waves in Large\u2010Scale Neuronal Networks","display_name":"Patterns and Features of Families of Traveling Waves in Large\u2010Scale Neuronal Networks","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1994762657","doi":"https://doi.org/10.1137/06066638x","mag":"1994762657"},"language":"en","primary_location":{"id":"doi:10.1137/06066638x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066638x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","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/A5054020432","display_name":"William C. Troy","orcid":"https://orcid.org/0000-0001-8924-245X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William C. Troy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044351239","display_name":"Vladimir Shusterman","orcid":"https://orcid.org/0000-0002-8516-4973"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vladimir Shusterman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1473,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.75946934,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"6","issue":"1","first_page":"263","last_page":"292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9994000196456909,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9991000294685364,"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/physics","display_name":"Physics","score":0.6469439268112183},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5979114770889282},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5378837585449219},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.45485949516296387},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4420351982116699},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.4207509160041809},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32757502794265747},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23476111888885498},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10822466015815735}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6469439268112183},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5979114770889282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5378837585449219},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.45485949516296387},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4420351982116699},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.4207509160041809},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32757502794265747},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23476111888885498},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10822466015815735}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/06066638x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066638x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","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":54,"referenced_works":["https://openalex.org/W292662503","https://openalex.org/W1489965517","https://openalex.org/W1530042053","https://openalex.org/W1536843209","https://openalex.org/W1577873058","https://openalex.org/W1584288643","https://openalex.org/W1646784260","https://openalex.org/W1750887975","https://openalex.org/W1848181806","https://openalex.org/W1869401664","https://openalex.org/W1896244601","https://openalex.org/W1923614344","https://openalex.org/W1963638114","https://openalex.org/W1963995097","https://openalex.org/W1970153575","https://openalex.org/W1970323478","https://openalex.org/W1978071915","https://openalex.org/W1992476998","https://openalex.org/W2016448450","https://openalex.org/W2029374903","https://openalex.org/W2033553753","https://openalex.org/W2042862694","https://openalex.org/W2046196779","https://openalex.org/W2048678256","https://openalex.org/W2064627393","https://openalex.org/W2070447195","https://openalex.org/W2071766364","https://openalex.org/W2074692696","https://openalex.org/W2080481491","https://openalex.org/W2081904428","https://openalex.org/W2089146894","https://openalex.org/W2092356747","https://openalex.org/W2096600960","https://openalex.org/W2097832960","https://openalex.org/W2099044759","https://openalex.org/W2101103067","https://openalex.org/W2101213717","https://openalex.org/W2101794949","https://openalex.org/W2102952547","https://openalex.org/W2106863426","https://openalex.org/W2121319723","https://openalex.org/W2129153032","https://openalex.org/W2131367668","https://openalex.org/W2142875089","https://openalex.org/W2157694985","https://openalex.org/W2160160303","https://openalex.org/W2160180788","https://openalex.org/W2169898855","https://openalex.org/W2223840560","https://openalex.org/W2502209207","https://openalex.org/W2600715701","https://openalex.org/W2614700606","https://openalex.org/W2990041661","https://openalex.org/W4250400713"],"related_works":["https://openalex.org/W3083820578","https://openalex.org/W2044927803","https://openalex.org/W2038494689","https://openalex.org/W2046520066","https://openalex.org/W2007879987","https://openalex.org/W2084329582","https://openalex.org/W4311946249","https://openalex.org/W2963061872","https://openalex.org/W2222735512","https://openalex.org/W2468364993"],"abstract_inverted_index":{"We":[0,49],"study":[1],"traveling":[2,98],"wave":[3,133,183,208],"solutions":[4],"of":[5,8,15,18,33,36,55,73,76,97,127,132,197,220,256],"a":[6,34,45,52,125,164,168,181,203],"system":[7,78],"integro\u2010differential":[9],"equations":[10],"which":[11,39,70,94,130],"describe":[12],"the":[13,29,56,65,71,74,77,80,101,107,113,190,194,212,230,251],"activity":[14,30],"large\u2010scale":[16],"networks":[17],"excitatory":[19,37],"neurons":[20],"on":[21,250],"spatially":[22,169],"extended":[23],"domains.":[24],"The":[25],"independent":[26],"variables":[27],"are":[28,103,115,234],"level":[31],"u":[32],"population":[35],"neurons,":[38],"have":[40,50],"long":[41],"range":[42,108,126],"connections,":[43],"and":[44,135,137,157,202,210,244],"recovery":[46],"variable":[47],"v.":[48],"found":[51],"critical":[53],"value":[54],"parameter":[57],"\u03b2":[58],"($\\beta_*":[59],">":[60,110],"0$)":[61],"that":[62,122,218,232,245],"appears":[63],"in":[64,161,229],"equation":[66],"for":[67],"v,":[68],"at":[69,226],"eigenvalues":[72,102,114],"linearization":[75],"around":[79],"rest":[81],"state":[82],"$(u,v)=(0,0)$":[83],"change":[84],"from":[85],"real":[86],"to":[87,91,163],"complex.":[88,116],"In":[89,117,147],"contrast":[90],"previous":[92],"studies":[93],"analyzed":[95],"properties":[96],"waves":[99,141,159,175,198],"when":[100,180],"real,":[104],"we":[105,120],"examine":[106],"$\\beta":[109],"\\beta_*$,":[111],"where":[112],"this":[118],"case":[119],"show":[121,154],"there":[123],"is":[124,192,216],"parameters":[128],"over":[129],"families":[131],"fronts":[134],"1\u2010pulse":[136],"more":[138],"general":[139],"N\u2010pulse":[140],"can":[142,176,223],"coexist":[143],"as":[144],"stable":[145,204],"solutions.":[146],"two":[148],"space":[149],"dimensions":[150],"our":[151],"numerical":[152],"experiments":[153],"how":[155],"single\u2010ring":[156],"multiring":[158],"form":[160],"response":[162],"Gaussian\u2010shaped":[165],"stimulus.":[166],"With":[167],"invariant":[170],"coupling":[171,191],"function,":[172],"outwardly":[173],"propagating":[174],"be":[177,224],"periodically":[178],"produced":[179],"ring\u2010shaped":[182],"receives":[184],"an":[185,238,257],"appropriately":[186],"timed":[187],"perturbation.":[188],"When":[189],"inhomogeneous":[193],"periodic":[195,242,254],"production":[196],"eventually":[199],"breaks":[200],"down,":[201],"one\u2010armed":[205],"rotating":[206],"spiral":[207],"emerges":[209],"fills":[211],"entire":[213],"domain.":[214],"It":[215],"noteworthy":[217],"all":[219],"these":[221],"phenomena":[222],"initiated":[225],"any":[227],"point":[228],"medium,":[231],"they":[233,246],"not":[235,248],"driven":[236],"by":[237],"underlying":[239],"time":[240],"dependent":[241],"pacemaker,":[243],"do":[247],"depend":[249],"persistent":[252],"or":[253],"presence":[255],"external":[258],"input.":[259]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
