More than two decades of intensive studies on non-linear dynamics have raised questions on the practical applications of chaos. One possible answer is to control chaotic behavior in a predictable way. This book, oneof the first on the subject, explores the ideas behind controlling chaos.
Controlling Chaos explains, using simple examples, both the mathematical theory and experimental results used to apply chaotic dynamics to real engineering systems. Chuas circuit is used as an example throughout the book as it can be easily constructed in the laboratory and numerically modeled. The use of this example allows readers to test the theories presented. The text is carefully balanced between theory and applications to provide an in-depth examination of the concepts behind the complex ideas presented. In the final section, Kapitaniak brings together selected reprinted papers which have had a significant effect on the development of this rapidly growing interdisciplinary field. Controlling Chaos is essential reading for graduates, researchers, and students wishing to be at the forefront of this exciting new branch of science.
- Uses easy examples which can be repeated by the reader both experimentally and numerically
- The first book to present basic methods of controlling chaos
- Includes reprinted papers representing fundamental contributions to the field
- Discusses implementation of chaos controlling fundamentals as applied to practical problems
Postgraduates and research workers in the fields of Aerospace, Civil, Mechanical, and Electrical Engineering, Applied Mathematics, Physics, and Meteorology.
Part I: General Outlook: Introduction. Controlling Chaos Through Feedback: Ott-Grebogi-Yorke Method. Pyragass and Classical Control Methods. Controlling Chaos by Chaos. Controlling Chaos without Feedback: Control Through Operating Conditions. Control by System Design. Taming Chaos. Entrainment and Migration Control. Syhnchronization of Chaos: Pecora and Carrolls Approach. Synchronization by Continuous Control. Monotonic Synchronization. Practical Synchronization. Synchronization in Quasi-Hyperbolic Systems. Secure Communication. Engineering Implementations: Method Selection. Occasional Proportional Feedback Method. Sampled Input Waveform Method. Controlling Transient Behavior in Mechanical Systems.Further Reading. References. Part II: Selected Reprints: E. Ott, C. Grebogi, and Y.A. Yorke, Controlling Chaos. F.J. Romeiras, C. Grebogi, E. Ott, and W.P. Dayawansa, Controlling Chaotic Dynamical Systems. U. Dressler and G. Nitsche, Controlling Chaos Using Time Delay Coordinates. W.L. Ditto, S.W. Rausco, and M.L. Spano, Experimental Control of Chaos. T. Tel, Controlling Transient Chaos. T. Shinbrot, E. Ott, C. Grebogi, and Y.A. Yorke, Using Chaos to DirectTrajectories to Targets. K. Pyragas, Continuous Control of Chaos by Self-Controlling Feedback. E.A. Jackson, On the Control of Complex Dynamic Systems. L.M. Pecora and T.L. Carroll, Synchronization in Chaotic Systems. K. Pyragas,Predictable Chaos in Slightly Perturbed Unpredictable Chaotic Systems. K.M. Cuomo, and A.V. Oppenheim, Circuit Implementation of Synchronized Chaos with Applications to Communications. G. Perez and H.A. Cerdeira, Extracting Messages Masked byChaos. K. Kocarev, and U. Parlitz, General Approach for Chaotic Synchronization with Applications to Communication. Index. Color Plate Section.
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- © Academic Press 1996
- 19th July 1996
- Academic Press
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Tomasz Kapitaniak is Professor of Mechanics and Head of the Dynamic Department at the Technical University of Lodz, Poland. In addition to his many published books and papers on chaos, Dr. Kapitaniak has lectured at several universities in Europe, North America, Asia and Africa.Kapitaniak was awarded the British Council Award Fellowship in 1989, and the King Abdul Aziz City of Science and Engineering Award Fellowship in 1990. He has been theauthor of numerous publications in the field of chaos dynamics, including three books. Kapitaniak earned his DSc in Theoretical and Applied Mechanics, his MSc in Mechanical Engineering and MSc in Math, and his PhD in Theoretical and Applied Mechanics from the University of Lodz. He has held positions as a Lecturer, Senior Lecturer, as well as Professor and head of the Division of Technology at the University of Lodz. He has also held a position as Visiting Research Professor at the University of Leeds.
Technical University of Lodz