{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:35:51Z","timestamp":1759091751320},"reference-count":41,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:p> It is known that border-collision bifurcations in piecewise-smooth maps can lead to situations where several attractors are created simultaneously in so-called \"multiple-attractor\" or \"multiple-choice\" bifurcations. It has been shown that such a situation leads to a fundamental source of uncertainty regarding which attractor the system will follow as a parameter is varied through the bifurcation point. Phenomena of this type have been observed in various physical and engineering systems. We have recently demonstrated that piecewise-smooth systems can exhibit a new type of border-collision bifurcation in which a stable invariant curve, associated with a quasiperiodic or a mode-locked periodic orbit, arises from a fixed point. In this paper we consider a particular variant of the multiple-attractor bifurcation in which a stable periodic orbit arises simultaneously with a closed invariant curve. We also show examples of simultaneously appearing stable periodic orbits and of the simultaneous generation of periodic and chaotic attractors. <\/jats:p>","DOI":"10.1142\/s0218127408021361","type":"journal-article","created":{"date-parts":[[2008,9,1]],"date-time":"2008-09-01T09:19:15Z","timestamp":1220260755000},"page":"1775-1789","source":"Crossref","is-referenced-by-count":21,"title":["MULTIPLE-ATTRACTOR BIFURCATIONS AND QUASIPERIODICITY IN PIECEWISE-SMOOTH MAPS"],"prefix":"10.1142","volume":"18","author":[{"given":"ZHANYBAI T.","family":"ZHUSUBALIYEV","sequence":"first","affiliation":[{"name":"Kursk State Technical University, Department of Computer Science, 50 Years of October Str., 94, Kursk 305040, Russia"}]},{"given":"ERIK","family":"MOSEKILDE","sequence":"additional","affiliation":[{"name":"Complex Systems Group, Department of Physics, Technical University of Denmark, 2800 Lyngby, Denmark"}]},{"given":"SOUMITRO","family":"BANERJEE","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Center for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, India"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/81.940187"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012946"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.4052"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/81.847870"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545393"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/3982"},{"key":"rf7","volume-title":"Nonsmooth Mechanics \u2014 Models, Dynamics and Control","author":"Brogliato B.","year":"1999"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1994.0049"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(01)00230-2"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2005.02.008"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/63.56516"},{"key":"rf12","first-page":"1881","volume":"10","author":"di Bernardo M.","journal-title":"Chaos Solit. 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