{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:52:41Z","timestamp":1770900761459,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p> This paper is concerned with the computation of the basins of attraction of a simple one degree-of-freedom backlash oscillator using cell-to-cell mapping techniques. This analysis is motivated by the modeling of order vibration in geared systems. We consider both a piecewise-linear stiffness model and a simpler infinite stiffness impacting limit. The basins reveal rich and delicate dynamics, and we analyze some of the transitions in the system's behavior in terms of smooth and discontinuity-induced bifurcations. The stretching and folding of phase space are illustrated via computations of the grazing curve, and its preimages, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit). <\/jats:p>","DOI":"10.1142\/s021812740902283x","type":"journal-article","created":{"date-parts":[[2009,3,20]],"date-time":"2009-03-20T10:36:08Z","timestamp":1237545368000},"page":"203-224","source":"Crossref","is-referenced-by-count":41,"title":["BASINS OF ATTRACTION IN NONSMOOTH MODELS OF GEAR RATTLE"],"prefix":"10.1142","volume":"19","author":[{"given":"JOANNA F.","family":"MASON","sequence":"first","affiliation":[{"name":"MACSI, Department of Mathematics &amp; Statistics, University of Limerick, Limerick, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PETRI T.","family":"PIIROINEN","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. EDDIE","family":"WILSON","sequence":"additional","affiliation":[{"name":"Bristol Centre for Applied Nonlinear Mathematics, University of Bristol, Bristol BS8 1TR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARTIN E.","family":"HOMER","sequence":"additional","affiliation":[{"name":"Bristol Centre for Applied Nonlinear Mathematics, University of Bristol, Bristol BS8 1TR, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"303","volume":"39","author":"Back A.","journal-title":"Notices Amer. Math. 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