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Bifurcations in piecewise-smooth continuous systems
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eBook
Bifurcations in piecewise-smooth continuous systems
2010
Overview
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.
Publisher
World Scientific Publishing Co. Pte. Ltd,World Scientific,World Scientific Publishing Company,WORLD SCIENTIFIC,World Scientific Publishing
Subject
ISBN
9789814293846, 9814293849, 9789814293853, 9814293857
