{"id":"https://openalex.org/W2093667188","doi":"https://doi.org/10.1142/s0218127412300261","title":"SELF-ORGANIZATION OF L\u00d6SCH'S HEXAGONS IN ECONOMIC AGGLOMERATION FOR CORE-PERIPHERY MODELS","display_name":"SELF-ORGANIZATION OF L\u00d6SCH'S HEXAGONS IN ECONOMIC AGGLOMERATION FOR CORE-PERIPHERY MODELS","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2093667188","doi":"https://doi.org/10.1142/s0218127412300261","mag":"2093667188"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127412300261","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412300261","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5031616318","display_name":"Kiyohiro Ikeda","orcid":"https://orcid.org/0000-0002-0291-4346"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"KIYOHIRO IKEDA","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Tohoku University, Aoba 6-6-06, Sendai 980-8579, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba 6-6-06, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032957138","display_name":"Kazuo Murota","orcid":"https://orcid.org/0000-0003-1518-9152"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"KAZUO MUROTA","raw_affiliation_strings":["Department of Mathematical Informatics, University of Tokyo, Tokyo 113-8656, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Informatics, University of Tokyo, Tokyo 113-8656, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086632927","display_name":"Takashi Akamatsu","orcid":"https://orcid.org/0000-0002-8545-839X"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"TAKASHI AKAMATSU","raw_affiliation_strings":["School of Information Sciences, Tohoku University, Aoba 6-6-06, Sendai 980-8579, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Sciences, Tohoku University, Aoba 6-6-06, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031616318"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":7.4108,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9681753,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"08","first_page":"1230026","last_page":"1230026"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11014","display_name":"Regional Economics and Spatial Analysis","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11014","display_name":"Regional Economics and Spatial Analysis","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9775000214576721,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/hexagonal-crystal-system","display_name":"Hexagonal crystal system","score":0.7017320394515991},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.6568182110786438},{"id":"https://openalex.org/keywords/economies-of-agglomeration","display_name":"Economies of agglomeration","score":0.6346715688705444},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.5345211625099182},{"id":"https://openalex.org/keywords/hexagonal-lattice","display_name":"Hexagonal lattice","score":0.527611255645752},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5226342678070068},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5009169578552246},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.47522762417793274},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.46874478459358215},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.45608019828796387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45008155703544617},{"id":"https://openalex.org/keywords/economic-geography","display_name":"Economic geography","score":0.4077494740486145},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3645482063293457},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3599013686180115},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3526919484138489},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33392244577407837},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.31510090827941895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24226394295692444},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.21890690922737122},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.12014502286911011},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10604047775268555},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.10369974374771118},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.08341780304908752},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.076515793800354}],"concepts":[{"id":"https://openalex.org/C128765274","wikidata":"https://www.wikidata.org/wiki/Q663314","display_name":"Hexagonal crystal system","level":2,"score":0.7017320394515991},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6568182110786438},{"id":"https://openalex.org/C131850264","wikidata":"https://www.wikidata.org/wiki/Q383056","display_name":"Economies of agglomeration","level":2,"score":0.6346715688705444},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.5345211625099182},{"id":"https://openalex.org/C90626534","wikidata":"https://www.wikidata.org/wiki/Q4523381","display_name":"Hexagonal lattice","level":3,"score":0.527611255645752},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5226342678070068},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5009169578552246},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.47522762417793274},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.46874478459358215},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.45608019828796387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45008155703544617},{"id":"https://openalex.org/C26271046","wikidata":"https://www.wikidata.org/wiki/Q187097","display_name":"Economic geography","level":1,"score":0.4077494740486145},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3645482063293457},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3599013686180115},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3526919484138489},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33392244577407837},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.31510090827941895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24226394295692444},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.21890690922737122},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.12014502286911011},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10604047775268555},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.10369974374771118},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.08341780304908752},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.076515793800354},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","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},{"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/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","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/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127412300261","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412300261","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W229452457","https://openalex.org/W1514319473","https://openalex.org/W1550812296","https://openalex.org/W1559000686","https://openalex.org/W1562427428","https://openalex.org/W1567092208","https://openalex.org/W1596185498","https://openalex.org/W1605188341","https://openalex.org/W1965778005","https://openalex.org/W1977106683","https://openalex.org/W1980412651","https://openalex.org/W1981476216","https://openalex.org/W1986769726","https://openalex.org/W2000829282","https://openalex.org/W2004247590","https://openalex.org/W2009124915","https://openalex.org/W2017398806","https://openalex.org/W2023351488","https://openalex.org/W2024476127","https://openalex.org/W2026169778","https://openalex.org/W2028407360","https://openalex.org/W2046299268","https://openalex.org/W2074062497","https://openalex.org/W2093550247","https://openalex.org/W2096913736","https://openalex.org/W2118486153","https://openalex.org/W2122329937","https://openalex.org/W2137569082","https://openalex.org/W2155358794","https://openalex.org/W2158923557","https://openalex.org/W2168699659","https://openalex.org/W2235184855","https://openalex.org/W2295626191","https://openalex.org/W2487249630","https://openalex.org/W2804470716","https://openalex.org/W2889260602","https://openalex.org/W3022519020","https://openalex.org/W3121519629","https://openalex.org/W4239404452","https://openalex.org/W4243592922","https://openalex.org/W4248132613","https://openalex.org/W4250872407","https://openalex.org/W4256046955","https://openalex.org/W4298006642","https://openalex.org/W4301283928"],"related_works":["https://openalex.org/W2963854314","https://openalex.org/W2157756491","https://openalex.org/W2063132333","https://openalex.org/W2766222296","https://openalex.org/W2274816674","https://openalex.org/W2017296099","https://openalex.org/W134821132","https://openalex.org/W2898187704","https://openalex.org/W2093667188","https://openalex.org/W629466858"],"abstract_inverted_index":{"Hexagonal":[0],"population":[1],"distributions":[2,48],"of":[3,22,95],"several":[4],"sizes":[5],"are":[6,34,53,73],"shown":[7],"to":[8,55],"be":[9,56],"self-organized":[10],"from":[11],"a":[12,20,26,37],"uniformly":[13],"inhabited":[14],"state,":[15],"which":[16],"is":[17],"modeled":[18],"by":[19,36,58,75],"system":[21],"places":[23,33],"(cities)":[24],"on":[25,62],"hexagonal":[27,47],"lattice.":[28],"Microeconomic":[29],"interactions":[30],"among":[31],"the":[32,96],"expressed":[35],"core-periphery":[38],"model":[39],"in":[40,49,93],"new":[41,86],"economic":[42,87],"geography.":[43],"L\u00f6sch's":[44],"ten":[45],"smallest":[46],"central":[50,82],"place":[51,83],"theory":[52,84],"guaranteed":[54],"existent":[57],"equivariant":[59],"bifurcation":[60,97],"analysis":[61],"D":[63],"6":[64],"\u2214":[65],"(\u2124":[66],"n":[67,70],"\u00d7":[68],"\u2124":[69],"),":[71],"and":[72,85],"obtained":[74],"computational":[76],"analysis.":[77,98],"The":[78],"missing":[79],"link":[80],"between":[81],"geography":[88],"has":[89],"thus":[90],"been":[91],"discovered":[92],"light":[94]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
