By Huaguang Zhang
Controlling Chaos deals its reader an intensive choice of options to accomplish 3 objectives: the suppression, synchronization and new release of chaos, each one of that's the point of interest of a separate a part of the e-book. The textual content offers with the well known Lorenz, Rössler and Hénon attractors and the Chua circuit, and with much less celebrated novel platforms. Modeling of chaos is entire utilizing distinction equations and traditional and time-delayed differential equations. The equipment directed at controlling chaos enjoy the effect of complicated nonlinear keep watch over thought: inverse optimum keep watch over is used for stabilization; specific 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 regulate of chaotic structures. Time-delayed platforms also are studied with many synchronization tools being explored. all of the effects offered are basic for a extensive classification of chaotic systems.
This monograph is self-contained with introductory fabric supplying a evaluate of the background of chaos regulate and the mandatory mathematical preliminaries for operating with dynamical systems.
Controlling Chaos may be of curiosity to teachers from electric, platforms, mechanical and chemical engineering backgrounds operating up to speed conception with regards to nonlinear dynamical and chaotic platforms and to graduate scholars of chaos control.
The Communications and keep an eye on Engineering sequence stories significant technological advances that have strength for nice influence within the fields of verbal exchange and regulate. It displays study in business and educational associations worldwide in order that the readership can take advantage of new percentages as they turn into available.
Read or Download Controlling Chaos: Suppression, Synchronization and Chaotification PDF
Similar system theory books
Cooperative keep watch over layout: a scientific, Passivity-Based technique discusses multi-agent coordination difficulties, together with formation keep watch over, perspective coordination, and contract. The e-book introduces passivity as a layout software for multi-agent structures, presents exemplary paintings utilizing this tool,and illustrates its benefits in designing strong cooperative keep an eye on algorithms.
From the experiences to the 1st variation: lots of the literature approximately stochastic differential equations turns out to put quite a bit emphasis on rigor and completeness that it scares the nonexperts away. those notes are an try and technique the topic from the nonexpert viewpoint. : now not realizing something .
The booklet contains a rigorous and self-contained remedy of initial-value difficulties for traditional differential equations. It also develops the fundamentals of regulate concept, that's a different function in present textbook literature. the next themes are relatively emphasised:• life, strong point and continuation of solutions,• non-stop dependence on preliminary data,• flows,• qualitative behaviour of solutions,• restrict sets,• balance theory,• invariance principles,• introductory keep watch over theory,• suggestions and stabilization.
- Econodynamics: The Theory of Social Production
- Truncated Predictor Feedback for Time-Delay Systems
- Stability Theory of Switched Dynamical Systems
- Linear Systems Theory
- Synchronization. A universal concept in nonlinear sciences
- From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift
Additional info for Controlling Chaos: Suppression, Synchronization and Chaotification
Phys Rev Lett 64:821–824 50. Pilovsky AS, Rosenblum MG, Kurths J (2001) Synchronization: A Universal Concepts in Nonlinear Science. Cambridge University Press, London 51. Pilovsky AS, Rosenblum MG, Osipov GV, Kurths J (1997) Phase synchronization of chaotic oscillators by external driving. Physica D 104:219–238 52. Pingel D, Schmelcher P, Diakonos FK, Biham O (2000) Theory and application of systematic detection of unstable periodic orbits in dynamical systems. Phys Rev E 62:2119–2134 53. Pingel D, Schmelcher P, Diakonos FK (2001) Detecting unstable periodic orbits in chaotic continuous-time dynamical systems.
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. Along this route, Wang studied further the problem of chaotification of continuous-time systems and he proposed a method which makes the outputs of the controlled system approximate the outputs of a chaotic system . (iii) Proving the existence of a Smale horseshoe.
11 (a) and (c), respectively, but arrows point in the opposite direction and the time order of points is reversed). In this case, the unstable eigenspace coincides with the state space. If |κ1 | > 1 and |κ2 | < 1 the fixed point is a saddle point. No sequences of points approach the equilibrium for n → ±∞ except for those originating from points on the eigenvectors associated with κ2 . Again, if κ1 , κ2 > 0 orbits move monotonically (see Fig. 11 (b)); otherwise they oscillate improperly (see Fig.
Controlling Chaos: Suppression, Synchronization and Chaotification by Huaguang Zhang