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Chaos in Electronics : Mathematical Modelling: Theory and Applications - M.A.Van Wyk

Chaos in Electronics

Mathematical Modelling: Theory and Applications


Published: 31st May 1997
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Many dynamical systems in physics, chemistry and biology exhibit complex be- haviour. The apparently random motion of a fluid is the best known example. How- ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim- plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla- tors is also included. End of proofs and examples are indicated by *. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.

List of Symbols
Introductionp. 1
Analysis of Chaotic Systemsp. 7
One-dimensional Maps in Electronicsp. 75
Higher Dimensional Maps in Electronicsp. 119
Autonomous Systems in Electronicsp. 171
Driven Systemsp. 221
Controlling Chaosp. 291
Chaos in Electronics: The Futurep. 341
One-Dimensional Mapsp. 343
Important Definitions and Theoremsp. 395
Mathematical Methodsp. 401
MATLAB Program Listingsp. 405
Bibliographyp. 415
Indexp. 475
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345763
ISBN-10: 0792345762
Series: Mathematical Modelling: Theory and Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 483
Published: 31st May 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 2.69
Weight (kg): 1.93