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. |
Contents
Controlling chaos without feedback | 3 |
Synchronization of chaos | 29 |
Engineering implementations | 53 |
Copyright | |
8 other sections not shown
Common terms and phrases
A₁ achieve control amplitude applied basin of attraction basin of entrainment BE(go behavior Bifurcat bifurcation C₁ C₂ Carroll chaos control chaotic attractor chaotic dynamical chaotic systems Chua's circuit conditional Lyapunov exponents control formula control method control of chaos control parameter Controlling chaos convergent region corresponding delay coordinates denote dimensional double rotor map dynamical system E(go eigenvalues embedded equations example experimental fixed point g₁ goal dynamics Grebogi Hénon map Hübler IEEE Trans illustrated information signal initial conditions iterate J.A. Yorke K₁ Kapitaniak Lett linear logistic map Lorenz system Lyapunov exponents m-goal matrix noise nonlinear obtained oscillator Pecora phase space Phys Physics regulator poles return map Rössler shown in Figure stabilization stable manifold subsystems surface of section synchronization synchronization of chaos target Theorem trajectories transient chaos transmitter unstable periodic orbits values variable vector x₁