{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:56:47Z","timestamp":1772290607976,"version":"3.50.1"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,5]]},"abstract":"<jats:p> In this paper, a piecewise map with singularity of the power (-1\/2) is introduced. For this piecewise map, there is an infinite discontinuous gap on the origin. The conditions of nonsmooth border-collision bifurcation and smooth fold or flip bifurcation are analytically derived. For period-1 fixed point, two-parameter-plane can be divided into seven ranges according to different bifurcation structures. For period-n orbits, codimension-2 bifurcation point may lead to different period-increment sequence, and a peculiar feature is found that there are two different period-increment sequences in the same bifurcation diagram. <\/jats:p>","DOI":"10.1142\/s021812741250112x","type":"journal-article","created":{"date-parts":[[2012,3,29]],"date-time":"2012-03-29T01:21:56Z","timestamp":1332984116000},"page":"1250112","source":"Crossref","is-referenced-by-count":10,"title":["NONSMOOTH AND SMOOTH BIFURCATIONS IN A DISCONTINUOUS PIECEWISE MAP"],"prefix":"10.1142","volume":"22","author":[{"given":"ZHIYING","family":"QIN","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YUEJING","family":"ZHAO","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JICHEN","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Dynamics and Control, Beihang University, Beijing 100091, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,28]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/81.841921"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00161-X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2005.01.046"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/81.873871"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(91)90592-8"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90087-4"},{"key":"rf7","first-page":"3341","volume":"13","author":"Parag J.","journal-title":"Int. J. Bifurcation and Chaos"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812741250112X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:13:58Z","timestamp":1565194438000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812741250112X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5]]},"references-count":7,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2012,6,28]]},"published-print":{"date-parts":[[2012,5]]}},"alternative-id":["10.1142\/S021812741250112X"],"URL":"https:\/\/doi.org\/10.1142\/s021812741250112x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5]]}}}