BIFURCATIONS and Chaos in Piecewise-Smooth Dynamical Systems

rockelin · 发表于 2014-11-28 09:41:08

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World Scientific Series on Nonlinear Science Series A: Volume 44
Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems
Applications to Power Converters, Relay and Pulse-Width Modulated Control Systems, and Human Decision-Making Behavior

对于研究本专业的人员，是比较经典的书。简介见下面。

封面

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.

Contents:

On the Dynamics of Nonlinear Systems
Basic Concepts and Methods
Relay Control Systems
Bifurcations and Chaotic Oscillations in Relay Systems
Chaotic Oscillations in Pulse-Width Modulated Systems
Border-Collision Bifurcations on a Two-Dimensional Torus
Border-Collision Bifurcations in a Management System

适用人群：

Readership: Graduate students and researchers in nonlinear science and chaos theory; electrical and electronic engineers; experts in control theory and in applied mathematics.