Chaos : concepts, control and constructive use / Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky.

Format:

Book

Author/Creator:

Bolotin, Yurii, author.

Tur, Anatoli, author.

Yanovsky, Vladimir, author.

Series:

Understanding complex systems

Springer complexity

Understanding complex systems, 1860-0832

Language:

English

Subjects (All):

Chaotic behavior in systems.

Physics.

System theory.

Computational complexity.

Vibration.

Dynamics.

Physical Description:

xi, 281 pages : illustrations, charts ; 25 cm.

Edition:

Second edition.

Place of Publication:

Cham : Springer, [2017]

Summary:

This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems ... The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.

Contents:

Introduction

Paradigm for Chaos

Main Features of Chaotic Systems

Reconstruction of Dynamical Systems

Controlling Chaos

Synchronization of Chaotic Systems

Stochastic Resonance

The Appearance of Regular Fluxes Without Gradients

Quantum Manifestations of Classical chaoticity

Tunneling and Chaos.

Notes:

Includes bibliographical references and index.

ISBN:

3319424955

9783319424958

OCLC:

951835046