Bifurcations In Piecewise-smooth Continuous Systems

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. NeimarkSacker-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.

List of contents

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;

Product details

• Authors: David John Warwick Simpson, David John Warwick Simpson, Simpson David John Warwick
• Publisher: Ingram Publishers Services
• Languages: English
• Product format: Hardback
• Released: 15.01.2010
• EAN: 9789814293846
• ISBN: 978-981-4293-84-6
• Series: World Scientific Series on Nonlinear Science Series A; World Scientific Series on Non; World Scientific Nonlinear Sci
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Miscellaneous; SCIENCE / Chaotic Behavior in Systems, Chaos Theory