Bifurcations in Piecewise-smooth Continuous Systems (repost)
David John Warwick Simpson, "Bifurcations in Piecewise-smooth Continuous Systems"
English | 2010-01-13 | ISBN: 9814293849 | 256 pages | PDF | 3.9 mb
English | 2010-01-13 | ISBN: 9814293849 | 256 pages | PDF | 3.9 mb
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.