000418205 000__ 02573cam\a2200397\a\4500 000418205 001__ 418205 000418205 005__ 20210513144746.0 000418205 006__ m\\\\\\\\u\\\\\\\\ 000418205 007__ cr\cn||||||||| 000418205 008__ 100927s2010\\\\njua\\\\sb\\\\001\0\eng\d 000418205 010__ $$z 2010484011 000418205 020__ $$z9789814293846 000418205 020__ $$z9814293849 000418205 020__ $$z9789814293853 (e-book) 000418205 035__ $$a(CaPaEBR)ebr10422400 000418205 035__ $$a(OCoLC)670429733 000418205 040__ $$aCaPaEBR$$cCaPaEBR 000418205 05014 $$aQA380$$b.S56 2010eb 000418205 08204 $$a515.35$$222 000418205 1001_ $$aSimpson, David John Warwick. 000418205 24510 $$aBifurcations in piecewise-smooth continuous systems$$h[electronic resource] /$$cDavid John Warwick Simpson. 000418205 260__ $$aNew Jersey :$$bWorld Scientific,$$c2010. 000418205 300__ $$axv, 238 p. :$$bill. (some col.) ;$$c24 cm. 000418205 4901_ $$aWorld Scientific series on nonlinear science. Series A, Monographs and treatises ;$$vv. 70 000418205 500__ $$aOriginally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. 000418205 504__ $$aIncludes bibliographical references (p. 215-235) and index. 000418205 506__ $$aAccess limited to authorized users. 000418205 520__ $$aReal-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. Neimark-Sacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems. 000418205 650_0 $$aBifurcation theory. 000418205 650_0 $$aDifferential equations. 000418205 650_0 $$aSaccharomyces cerevisiae. 000418205 655_7 $$aElectronic books.$$2lcsh 000418205 830_0 $$aWorld Scientific series on nonlinear science.$$nSeries A,$$pMonographs and treatises ;$$vv. 70. 000418205 852__ $$bebk 000418205 85640 $$3ProQuest Ebook Central Academic Complete$$uhttps://univsouthin.idm.oclc.org/login?url=http://site.ebrary.com/lib/usiricelib/Doc?id=10422400$$zOnline Access 000418205 909CO $$ooai:library.usi.edu:418205$$pGLOBAL_SET 000418205 980__ $$aEBOOK 000418205 980__ $$aBIB 000418205 982__ $$aEbook 000418205 983__ $$aOnline