{"id":"https://openalex.org/W1987660639","doi":"https://doi.org/10.1137/s0036139998340650","title":"Influence of Boundary Conditions on Pattern Formation and Spatial Chaos in Lattice Systems","display_name":"Influence of Boundary Conditions on Pattern Formation and Spatial Chaos in Lattice Systems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1987660639","doi":"https://doi.org/10.1137/s0036139998340650","mag":"1987660639"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139998340650","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139998340650","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/A5085085426","display_name":"Chih-Wen Shih","orcid":"https://orcid.org/0000-0001-8530-3542"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chih-Wen Shih","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085085426"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1445,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.88800375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"61","issue":"1","first_page":"335","last_page":"368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9995999932289124,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/lattice","display_name":"Lattice (music)","score":0.7203311920166016},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.6423780918121338},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6136786341667175},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6134296655654907},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"Pattern formation","score":0.5252406597137451},{"id":"https://openalex.org/keywords/coupled-map-lattice","display_name":"Coupled map lattice","score":0.4942379295825958},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4600526988506317},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.42217424511909485},{"id":"https://openalex.org/keywords/particle-in-a-one-dimensional-lattice","display_name":"Particle in a one-dimensional lattice","score":0.41031432151794434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3667680323123932},{"id":"https://openalex.org/keywords/lattice-field-theory","display_name":"Lattice field theory","score":0.27622053027153015},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21182718873023987},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18090838193893433},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.10184675455093384},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08539548516273499},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07623046636581421}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7203311920166016},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.6423780918121338},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6136786341667175},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6134296655654907},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.5252406597137451},{"id":"https://openalex.org/C39630112","wikidata":"https://www.wikidata.org/wiki/Q5178018","display_name":"Coupled map lattice","level":5,"score":0.4942379295825958},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4600526988506317},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.42217424511909485},{"id":"https://openalex.org/C129168087","wikidata":"https://www.wikidata.org/wiki/Q178825","display_name":"Particle in a one-dimensional lattice","level":4,"score":0.41031432151794434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3667680323123932},{"id":"https://openalex.org/C42238305","wikidata":"https://www.wikidata.org/wiki/Q5370778","display_name":"Lattice field theory","level":3,"score":0.27622053027153015},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21182718873023987},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18090838193893433},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.10184675455093384},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08539548516273499},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07623046636581421},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139998340650","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139998340650","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:bibcyt.ucla.edu.ve:T070300010470/15","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300010470/15&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6200000047683716,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W197647734","https://openalex.org/W258902366","https://openalex.org/W634029892","https://openalex.org/W653059893","https://openalex.org/W1546318328","https://openalex.org/W1557040331","https://openalex.org/W1964953733","https://openalex.org/W1970739133","https://openalex.org/W1974011730","https://openalex.org/W1974042224","https://openalex.org/W1981987846","https://openalex.org/W1982312043","https://openalex.org/W1993693726","https://openalex.org/W2034476467","https://openalex.org/W2036458635","https://openalex.org/W2037740421","https://openalex.org/W2042582506","https://openalex.org/W2046738125","https://openalex.org/W2047019301","https://openalex.org/W2051247954","https://openalex.org/W2056561971","https://openalex.org/W2056717940","https://openalex.org/W2062011896","https://openalex.org/W2068597145","https://openalex.org/W2076585865","https://openalex.org/W2084858355","https://openalex.org/W2090248486","https://openalex.org/W2095639497","https://openalex.org/W2103893462","https://openalex.org/W2107025852","https://openalex.org/W2109384700","https://openalex.org/W2110120048","https://openalex.org/W2151162785","https://openalex.org/W2160121923","https://openalex.org/W2171925415","https://openalex.org/W2602669193"],"related_works":["https://openalex.org/W2086238852","https://openalex.org/W2021821626","https://openalex.org/W2130946900","https://openalex.org/W1606282725","https://openalex.org/W2791104707","https://openalex.org/W2799999517","https://openalex.org/W2022869947","https://openalex.org/W2064651143","https://openalex.org/W70306223","https://openalex.org/W1987660639"],"abstract_inverted_index":{"This":[0,110],"work":[1],"elucidates":[2],"the":[3,16,43,68,73,94,116,122,131,157],"spatial":[4,40,103],"structure":[5],"of":[6,15,35,70,96],"lattice":[7,44,138,144],"dynamical":[8],"systems,":[9],"which":[10],"is":[11,49,64,108,112],"represented":[12],"by":[13,114,120],"equilibria":[14],"systems.":[17],"On":[18,90,148],"a":[19,57,77,91,135,149],"finite":[20,143],"lattice,":[21,93,151],"various":[22],"boundary":[23,31,97,146,158],"conditions":[24,32,98],"are":[25,54,87],"imposed.":[26],"The":[27,163],"effect":[28,63,159],"from":[29],"these":[30,71],"on":[33,82,99,134,140],"formation":[34,101],"pattern":[36,100],"as":[37,39,42,56],"well":[38],"complexity,":[41],"size":[45],"tends":[46],"to":[47,59],"infinity,":[48],"investigated.":[50],"Two":[51],"general":[52],"propositions":[53],"proposed":[55],"criteria":[58,118],"demonstrate":[60,155],"that":[61,156],"this":[62,168],"negligible.":[65,109],"To":[66],"illustrate":[67],"effectiveness":[69],"criteria,":[72],"mosaic":[74,106,132],"patterns":[75,107,133],"in":[76,167,176],"cellular":[78,177],"neural":[79,178],"network":[80],"model":[81],"one-":[83],"and":[84,102,119,139,165],"two-dimensional":[85,150],"lattices":[86],"also":[88],"studied.":[89],"one-dimensional":[92,136,142],"influence":[95],"chaos":[104],"for":[105,173],"result":[111],"justified":[113],"verifying":[115],"above-mentioned":[117],"using":[121],"transition":[123],"matrices.":[124],"These":[125],"appropriately":[126],"formulated":[127],"matrices":[128],"generate":[129],"all":[130],"infinite":[137],"any":[141],"with":[145],"conditions.":[147],"two":[152],"illustrative":[153],"examples":[154],"can":[160],"be":[161],"dominant.":[162],"results":[164],"analysis":[166],"investigation":[169],"have":[170],"significant":[171],"implications":[172],"circuit":[174],"design":[175],"networks.":[179]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}