Bifurcations in Piecewise-Smooth Continuous Systems

Bifurcations in Piecewise-Smooth Continuous Systems


by David John Warwick Simpson(ed.)

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.

World Scientific Publishing Company; January 2010 256 pages; ISBN 9789814465731 Read online , or download in secure PDF format Title: Bifurcations in Piecewise-Smooth Continuous Systems Author: David John Warwick Simpson   Buy, download and read Bifurcations in Piecewise-Smooth Continuous Systems (eBook) by David John Warwick Simpson today!
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