Author : David John Warwick Simpson
Publisher : World Scientific
ISBN 13 : 9814465739
Total Pages : 255 pages
Book Rating : 4.31/5 ( download)
Book Synopsis Bifurcations In Piecewise-smooth Continuous Systems by : David John Warwick Simpson
Download or read book Bifurcations In Piecewise-smooth Continuous Systems written by David John Warwick Simpson and published by World Scientific. This book was released on 2010-01-13 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.