Bifurcations And Chaos In Piecewise-smooth Dynamical Systems: Applications To Power Converters, Relay And Pulse-width Modulated Control Systems, And ... Series on Nonlinear Science Series A) - Hardcover

Zhusubaliyev, Zhanybai T; Mosekilde, Erik

Hardcover

ISBN 10: 9812384200 ISBN 13: 9789812384201

Publisher: World Scientific Publishing Co Pte Ltd, 2003

Synopsis

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems. In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

About this title

Review

.,." contains interesting examples of piecewise-smooth dynamical systems ... a useful tool for many scientists and engineers.?

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 2003
• ISBN 10: 9812384200
• ISBN 13: 9789812384201
• Binding: Hardcover
• Language: English
• Number of pages: 376