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We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.<\/jats:p>","DOI":"10.1063\/1.4767672","type":"journal-article","created":{"date-parts":[[2012,12,15]],"date-time":"2012-12-15T00:42:36Z","timestamp":1355532156000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":44,"title":["Combinatorial-topological framework for the analysis of global dynamics"],"prefix":"10.1063","volume":"22","author":[{"given":"Justin","family":"Bush","sequence":"first","affiliation":[{"name":"Department of Mathematics 1 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"},{"name":"The State University of New Jersey 1 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"}]},{"given":"Marcio","family":"Gameiro","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancias Matem\u00e1ticas e de Computa\u00e7\u00e3o, Universidade de S\u00e3o Paulo 2 , Caixa Postal 668, 13560-970 S\u00e3o Carlos, SP, Brazil"}]},{"given":"Shaun","family":"Harker","sequence":"additional","affiliation":[{"name":"Department of Mathematics 1 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"},{"name":"The State University of New Jersey 1 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"}]},{"given":"Hiroshi","family":"Kokubu","sequence":"additional","affiliation":[{"name":"Department of Mathematics\/JST CREST, Kyoto University 3 , Kyoto 606-8502, Japan"}]},{"given":"Konstantin","family":"Mischaikow","sequence":"additional","affiliation":[{"name":"Department of Mathematics 1 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"},{"name":"The State University of New Jersey 1 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"},{"name":"BioMaPS 4 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"},{"name":"The State University of New Jersey 4 , Hill Center-Busch Campus, Rutgers, , 110 Frelinghusen Rd, Piscataway, New Jersey 08854-8019, USA"}]},{"given":"Ippei","family":"Obayashi","sequence":"additional","affiliation":[{"name":"Department of Mathematics\/JST CREST, Kyoto University 3 , Kyoto 606-8502, Japan"}]},{"given":"Pawe\u0142","family":"Pilarczyk","sequence":"additional","affiliation":[{"name":"Centre of Mathematics, University of Minho 5 , Campus de Gualtar, 4710-057 Braga, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2012,12,14]]},"reference":[{"key":"2023070318250158100_c1","first-page":"225","article-title":"Graph-based topological approximation of saddle-node bifurcation in maps","volume":"31","year":"2012","journal-title":"RIMS Kokyuroku Bessatsu"},{"key":"2023070318250158100_c2","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1137\/080734935","article-title":"A database schema for the analysis of global dynamics of multiparameter systems","volume":"8","year":"2009","journal-title":"SIAM J. 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