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E-raamat: Bifurcations In Piecewise-smooth Continuous Systems

(Univ Of British Columbia, Usa)
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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.
Fundamentals of Piecewise-Smooth, Continuous Systems; Discontinuous
Bifurcations in Planar Systems; Codimension-Two, Discontinuous Bifurcations;
The Growth of Saccharomyces cerevisiae; Codimension-Two, Border-Collision
Bifurcations; Periodic Solutions and Resonance Tongues; Neimark-Sacker-Like
Bifurcations;