Chaos: Concepts, Control and Constructive Use

1. Front Matter

   Pages i-viii

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2. Introduction

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 1-3

3. Paradigm for Chaos

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 5-18

4. Main Features of Chaotic Systems

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 19-34

5. Reconstruction of Dynamical Systems

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 35-50

6. Controlling Chaos

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 51-99

7. Synchronization of Chaotic Systems

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 101-133

8. Stochastic Resonance

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 135-157

9. The Appearance of Regular Fluxes Without Gradients

   • Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky

   Pages 159-188

10. Back Matter

    Pages 1-10

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The study of physics has changed in character, mainly due to the passage from the analyses of linear systems to the analyses of nonlinear systems. Such a change began, it goes without saying, a long time ago but the qualitative change took place and boldly evolved after the understanding of the nature of chaos in nonlinear s- tems. The importance of these systems is due to the fact that the major part of physical reality is nonlinear. Linearity appears as a result of the simpli?cation of real systems, and often, is hardly achievable during the experimental studies. In this book, we focus our attention on some general phenomena, naturally linked with nonlinearity where chaos plays a constructive part. The ?rst chapter discusses the concept of chaos. It attempts to describe the me- ing of chaos according to the current understanding of it in physics and mat- matics. The content of this chapter is essential to understand the nature of chaos and its appearance in deterministic physical systems. Using the Turing machine, we formulate the concept of complexity according to Kolmogorov. Further, we state the algorithmic theory of Kolmogorov–Martin-Lof ¨ randomness, which gives a deep understanding of the nature of deterministic chaos. Readers will not need any advanced knowledge to understand it and all the necessary facts and de?nitions will be explained.

• chaos
• chaos control
• mechanics
• reconstruction of dynamical systems
• resonance
• stochastic resonance
• synchronization in complex systems
• system
• complexity

From the reviews:

“This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems in order to reach a large audience from science and engineering. The presentation is organized in 8 chapters. … 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 likes to grasp quickly the main issues related to chaos in discrete and continuous time.” (Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010)

• Technology, Kharkov Institute of Physics &, Kharkov, Ukraine

  Yurii Bolotin

• Rayonnements (CESR), Centre d'Étude Spatiale des, Toulouse CX 04, France

  Anatoli Tur

• SSI Institute for Single Crystals, National Academy of Sciences of Ukraine, Kharkov, Ukraine

  Vladimir Yanovsky

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