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These structures are formed by periodicity regions related to attracting cycles, namely, the skew tent map structure is associated with periodic points on two adjacent branches of the map, the period adding structure is related to periodic points on the outermost branches, and the fin structure is contiguous with the period adding structure and is associated with attracting cycles having at most one point on the middle branch. Analytical expressions for the periodicity region boundaries are obtained using the map replacement technique. <\/jats:p>","DOI":"10.1142\/s0218127413300401","type":"journal-article","created":{"date-parts":[[2014,1,7]],"date-time":"2014-01-07T02:29:22Z","timestamp":1389061762000},"page":"1330040","source":"Crossref","is-referenced-by-count":27,"title":["BIFURCATION STRUCTURES IN A BIMODAL PIECEWISE LINEAR MAP: REGULAR DYNAMICS"],"prefix":"10.1142","volume":"23","author":[{"given":"ANASTASIIA","family":"PANCHUK","sequence":"first","affiliation":[{"name":"Institute of Mathematics, NAS of Ukraine, Tereshchenkivska Str. 3, 01601 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"IRYNA","family":"SUSHKO","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, NAS of Ukraine, Tereshchenkivska Str. 3, 01601 Kyiv, Ukraine"},{"name":"Kyiv School of Economics, Yakira Str. 13, 04119 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BJ\u00d6RN","family":"SCHENKE","sequence":"additional","affiliation":[{"name":"Institute of Parallel and Distributed Systems, University of Stuttgart, Universit\u00e4tsstra\u00dfe 38, D-70569 Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VIKTOR","family":"AVRUTIN","sequence":"additional","affiliation":[{"name":"DESP, University of Urbino, Via Saffi 42, 61029 Urbino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,1,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410027581"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/81.841921"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545393"},{"key":"rf4","volume-title":"Nonlinear Oligopolies: Stability and Bifurcations","author":"Bischi G. 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