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Attention is paid to the existence of invariant solutions that retain their spatial patterns when the bifurcation parameter changes. Such existence is a special feature of the replicator dynamics, which is widely used in economics. A theoretical procedure to find invariant patterns is proposed and possible invariant patterns are advanced and classified. Among a plethora of theoretically possible invariant patterns, those which actually become stable for a spatial economic model are investigated numerically. The major finding of this paper, is the demonstration of equilibrium curves of invariant patterns that are connected by those of noninvariant ones to form a complicated mesh-like structure, just like the threads of warp and weft. It would be an important scientific mission to elucidate the mechanism of this complicated structure, and contribute to the study in economic geography.<\/jats:p>","DOI":"10.1142\/s0218127419300143","type":"journal-article","created":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T07:08:51Z","timestamp":1561964931000},"page":"1930014","source":"Crossref","is-referenced-by-count":9,"title":["Invariant Patterns for Replicator Dynamics on a Hexagonal Lattice"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0291-4346","authenticated-orcid":false,"given":"K.","family":"Ikeda","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"Kogure","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Aizawa","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"Takayama","sequence":"additional","affiliation":[{"name":"Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,7]]},"reference":[{"key":"S0218127419300143BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2012.04.010"},{"key":"S0218127419300143BIB002","doi-asserted-by":"crossref","DOI":"10.1515\/9781400841233","volume-title":"Economic Geography and Public Policy","author":"Baldwin R.","year":"2003"},{"key":"S0218127419300143BIB003","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0136248"},{"volume-title":"Fractal Cities","year":"1994","author":"Batty M.","key":"S0218127419300143BIB004"},{"key":"S0218127419300143BIB005","first-page":"1309","volume":"11","author":"B\u00e9nard H.","year":"1900","journal-title":"Rev. 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