## Controlling Chaos: Theoretical and Practical Methods in Non- Linear DynamicsMore 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 |

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### Contents

Introduction | 3 |

Controlling chaos without feedback | 17 |

Synchronization of chaos | 29 |

Copyright | |

8 other sections not shown

### Common terms and phrases

achieve control amplitude applied basin of attraction basin of entrainment Bifurcat bifurcation chaos control chaotic attractor chaotic behavior chaotic dynamical chaotic systems chaotic transient Chua Chua's circuit conditional Lyapunov exponents consider control formula control method control of chaos control parameter Controlling chaos convergent region corresponding coupled delay coordinates denote described dimensional double rotor map dynamical system eigenvalues embedded equations example experimental feedback control fixed point function goal dynamics Grebogi Henon map Hiibler IEEE Trans illustrated information signal initial conditions iterate J.A. Yorke Kapitaniak Lett linear logistic map Lorenz system Lyapunov exponents m-goal matrix monotone synchronization noise nonlinear obtained oscillator period-two phase space Phys Physics positive Lyapunov exponents return map Rossler system shown in Figure stabilization stable manifold subsystem surface of section switching synchronization of chaos Syst system parameter target Theorem trajectory transient chaos unstable periodic orbits values variables vector