{"id":"https://openalex.org/W2898187704","doi":"https://doi.org/10.1142/s0218127418501389","title":"Stability of Bifurcating Patterns of Spatial Economy Models on a Hexagonal Lattice","display_name":"Stability of Bifurcating Patterns of Spatial Economy Models on a Hexagonal Lattice","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2898187704","doi":"https://doi.org/10.1142/s0218127418501389","mag":"2898187704"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127418501389","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127418501389","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127418501389","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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":true,"oa_status":"hybrid","oa_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127418501389","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/I10091056","display_name":"Kanazawa University","ror":"https://ror.org/02hwp6a56","country_code":"JP","type":"education","lineage":["https://openalex.org/I10091056"]},{"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":"K. Ikeda","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan"],"raw_orcid":"https://orcid.org/0000-0002-0291-4346","affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan","institution_ids":["https://openalex.org/I10091056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077442961","display_name":"Hiroki Aizawa","orcid":"https://orcid.org/0000-0002-0929-6325"},"institutions":[{"id":"https://openalex.org/I10091056","display_name":"Kanazawa University","ror":"https://ror.org/02hwp6a56","country_code":"JP","type":"education","lineage":["https://openalex.org/I10091056"]},{"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":"H. Aizawa","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan","institution_ids":["https://openalex.org/I10091056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022741078","display_name":"Yosuke Kogure","orcid":"https://orcid.org/0000-0003-1326-6679"},"institutions":[{"id":"https://openalex.org/I10091056","display_name":"Kanazawa University","ror":"https://ror.org/02hwp6a56","country_code":"JP","type":"education","lineage":["https://openalex.org/I10091056"]},{"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":"Y. Kogure","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan","institution_ids":["https://openalex.org/I10091056"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072236529","display_name":"Yuki Takayama","orcid":"https://orcid.org/0000-0002-7638-4640"},"institutions":[{"id":"https://openalex.org/I10091056","display_name":"Kanazawa University","ror":"https://ror.org/02hwp6a56","country_code":"JP","type":"education","lineage":["https://openalex.org/I10091056"]},{"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":"Y. Takayama","raw_affiliation_strings":["Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan","Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan","institution_ids":["https://openalex.org/I10091056"]},{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072236529"],"corresponding_institution_ids":["https://openalex.org/I10091056","https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":3.8688,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.94393222,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"11","first_page":"1850138","last_page":"1850138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11014","display_name":"Regional Economics and Spatial Analysis","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9778000116348267,"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/T13402","display_name":"Business Strategy and Innovation","score":0.942300021648407,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7752389311790466},{"id":"https://openalex.org/keywords/hexagonal-crystal-system","display_name":"Hexagonal crystal system","score":0.6073429584503174},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5697224140167236},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5313584804534912},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5301371812820435},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5049074292182922},{"id":"https://openalex.org/keywords/spatial-ecology","display_name":"Spatial ecology","score":0.4999732971191406},{"id":"https://openalex.org/keywords/hexagonal-lattice","display_name":"Hexagonal lattice","score":0.4661406874656677},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.44724833965301514},{"id":"https://openalex.org/keywords/scalar-field","display_name":"Scalar field","score":0.42704877257347107},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.41653937101364136},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24705225229263306},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20528468489646912},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1613389551639557},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.1282309889793396},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11293229460716248},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.0658157467842102}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7752389311790466},{"id":"https://openalex.org/C128765274","wikidata":"https://www.wikidata.org/wiki/Q663314","display_name":"Hexagonal crystal system","level":2,"score":0.6073429584503174},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5697224140167236},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5313584804534912},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5301371812820435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5049074292182922},{"id":"https://openalex.org/C158709400","wikidata":"https://www.wikidata.org/wiki/Q3578586","display_name":"Spatial ecology","level":2,"score":0.4999732971191406},{"id":"https://openalex.org/C90626534","wikidata":"https://www.wikidata.org/wiki/Q4523381","display_name":"Hexagonal lattice","level":3,"score":0.4661406874656677},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.44724833965301514},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.42704877257347107},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.41653937101364136},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24705225229263306},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20528468489646912},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1613389551639557},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1282309889793396},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11293229460716248},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.0658157467842102},{"id":"https://openalex.org/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127418501389","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127418501389","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127418501389","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:t2r2.star.titech.ac.jp:50656438","is_oa":false,"landing_page_url":"http://t2r2.star.titech.ac.jp/cgi-bin/publicationinfo.cgi?q_publication_content_number=CTT100893812","pdf_url":null,"source":{"id":"https://openalex.org/S4377196385","display_name":"Tokyo Tech Research Repository (Tokyo Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114531698","host_organization_name":"Tokyo Institute of Technology","host_organization_lineage":["https://openalex.org/I114531698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1142/s0218127418501389","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127418501389","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127418501389","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2898187704.pdf","grobid_xml":"https://content.openalex.org/works/W2898187704.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1559000686","https://openalex.org/W1965778005","https://openalex.org/W1981476216","https://openalex.org/W1986769726","https://openalex.org/W1996121945","https://openalex.org/W2000829282","https://openalex.org/W2024476127","https://openalex.org/W2027538922","https://openalex.org/W2028407360","https://openalex.org/W2040032091","https://openalex.org/W2056836580","https://openalex.org/W2076096217","https://openalex.org/W2081489132","https://openalex.org/W2093667188","https://openalex.org/W2120366814","https://openalex.org/W2121546766","https://openalex.org/W2122329937","https://openalex.org/W2134393106","https://openalex.org/W2134717662","https://openalex.org/W2137569082","https://openalex.org/W2158923557","https://openalex.org/W2168699659","https://openalex.org/W2221358880","https://openalex.org/W2464777200","https://openalex.org/W2487249630","https://openalex.org/W3022519020","https://openalex.org/W4231092427","https://openalex.org/W4243592922","https://openalex.org/W4250872407","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2048324641","https://openalex.org/W2087433219","https://openalex.org/W2161086483","https://openalex.org/W3100111582","https://openalex.org/W2021251948","https://openalex.org/W2501825594","https://openalex.org/W2009267082","https://openalex.org/W1971364352","https://openalex.org/W2008081984","https://openalex.org/W2103399401"],"abstract_inverted_index":{"Self-organization":[0],"of":[1,10,13],"spatial":[2,43,59],"patterns":[3,34,65],"is":[4,22],"investigated":[5],"for":[6,41],"a":[7,11,16,58],"scalar":[8],"field":[9],"system":[12],"locations":[14,54],"on":[15],"hexagonal":[17],"lattice.":[18],"Group-theoretic":[19],"bifurcation":[20,73],"analysis":[21],"conducted":[23],"to":[24,37,68],"exhaustively":[25],"try":[26],"and":[27,62],"find":[28],"possible":[29],"bifurcating":[30,64],"patterns.":[31],"All":[32],"these":[33],"are":[35,55,66],"proved":[36],"be":[38,69],"asymptotically":[39],"unstable":[40,70],"general":[42],"economic":[44,48],"models":[45],"in":[46],"new":[47],"geography.":[49],"Microeconomic":[50],"interactions":[51],"among":[52],"the":[53],"expressed":[56],"by":[57,71],"economy":[60],"model":[61],"all":[63],"demonstrated":[67],"numerical":[72],"analysis.":[74]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}