Controlling Chaos

Theoretical and Practical Methods in Non-linear Dynamics


  • Tomasz Kapitaniak, Technical University of Lodz

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.
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Postgraduates and research workers in the fields of Aerospace, Civil, Mechanical, and Electrical Engineering, Applied Mathematics, Physics, and Meteorology.


Book information

  • Published: July 1996
  • ISBN: 978-0-12-396840-1

Table of Contents

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.