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- 2010484011 abstract "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.".
- 2010484011 contributor B11986261.
- 2010484011 created "2010.".
- 2010484011 date "2010".
- 2010484011 date "2010.".
- 2010484011 dateCopyrighted "2010.".
- 2010484011 description "Includes bibliographical references (p. 215-235) and index.".
- 2010484011 description "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.".
- 2010484011 extent "xv, 238 p. :".
- 2010484011 identifier "9789814293846".
- 2010484011 identifier "9814293849".
- 2010484011 isPartOf "World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70".
- 2010484011 isPartOf "World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70.".
- 2010484011 issued "2010".
- 2010484011 issued "2010.".
- 2010484011 language "eng".
- 2010484011 publisher "New Jersey : World Scientific,".
- 2010484011 subject "515.35 22".
- 2010484011 subject "Bifurcation theory.".
- 2010484011 subject "Differential equations.".
- 2010484011 subject "QA380 .S56 2010".
- 2010484011 subject "Saccharomyces cerevisiae.".
- 2010484011 title "Bifurcations in piecewise-smooth continuous systems / David John Warwick Simpson.".
- 2010484011 type "text".