Controlling Chaos: Suppression, Synchronization and by Huaguang Zhang

By Huaguang Zhang

Controlling Chaos bargains its reader an intensive choice of ideas to accomplish 3 pursuits: the suppression, synchronization and new release of chaos, every one of that's the point of interest of a separate a part of the ebook. The textual content bargains with the well known Lorenz, Rössler and Hénon attractors and the Chua circuit, and with much less celebrated novel structures. Modeling of chaos is complete utilizing distinction equations and traditional and time-delayed differential equations. The equipment directed at controlling chaos enjoy the impression of complex nonlinear keep an eye on concept: inverse optimum keep watch over is used for stabilization; designated linearization for synchronization; and impulsive keep watch over for chaotification. particularly, a fusion of chaos and fuzzy structures theories is hired, with the Takagi–Sugeno version and the authors’ personal fuzzy hyperbolic version used in the modeling and keep an eye on of chaotic structures. Time-delayed platforms also are studied with many synchronization equipment being explored. the entire effects provided are common for a extensive type of chaotic systems.

This monograph is self-contained with introductory fabric delivering a assessment of the heritage of chaos keep an eye on and the mandatory mathematical preliminaries for operating with dynamical systems.

Controlling Chaos may be of curiosity to teachers from electric, structures, mechanical and chemical engineering backgrounds operating up to the mark thought relating to nonlinear dynamical and chaotic structures and to graduate scholars of chaos control.

The Communications and keep an eye on Engineering sequence experiences significant technological advances that have capability for excellent impression within the fields of conversation and keep watch over. It displays study in commercial and educational associations around the globe in order that the readership can make the most new chances as they develop into available.

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Extra resources for Controlling Chaos: Suppression, Synchronization and Chaotification

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An attractor is a topologically transitive attracting set. 6 Continuous-Time Systems in the Plane In this section and the next two sections we will discuss the types of equilibrium points of planar systems of continuous time and discrete time, respectively. In applications, we very often encounter linear systems described by two first-order differential equations (or a differential equation of second order), either because the underlying model is linear or because it is linearized around an equilibrium point.

Chaotic). Poincar´e’s point of view was enthusiastically adopted and developed by G. D. Birkhoff. He found many different types of long-term limiting behavior. His work resulted in the book [4] from which the term ‘dynamical systems’ came. Other people, such as Lyapunov, Pontryagin, Andronov, Morser, Smale, Peixoto, Kolmogorov, Arnol’d, Sinai, Lorenz, May, Yorke, Feigenbaum, Ruelle, and Takens, all made important contributions to the theory of dynamical systems. The field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breakthroughs in science in the 20th century.

The system is excited by impulses at discrete instants. The impulsive signal is composed of two parts. One part is to eliminate the original motion, the other part is to make the system chaotic. Usually, this part is composed of chaotic signals [78]. c. Introducing time delay. This method is based on the following idea: the introduction of time delay makes a finite-dimensional system become an infinite-dimensional system. Thus, it is possible to produce more complicated behavior within it, especially chaos.

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