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0 (hodnocen0 x )

EB

ONLINE

New Jersey : World Scientific, 2010

1 online resource (xv, 238 p.) : ill. (some col.)

ISBN 9789814293853 (electronic bk.)

ISBN 9789814293846

ISBN 9814293849

World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70

Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008

Includes bibliographical references (p. 215-235) and index

Real-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..

Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries

001730764

full

(Au-PeEL)EBL731331

(CaONFJC)MIL276342

(CaPaEBR)ebr10422400

(MiAaPQ)EBC731331

(OCoLC)670429733