High-Dimensional Chaotic and Attractor Systems: A Comprehensive Introduction / Edition 1

by Vladimir G. Ivancevic, Tijana T. Ivancevic

Overview

If we try to describe real world in mathematical terms, we will see that real life is very often a high–dimensional chaos. Sometimes, by ‘pushing hard’, we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this high–dimensional chaotic dynamics of life. This is the main theme of the present book. In our previous book, Geometrical - namics of Complex Systems, Vol. 31 in Springer book series Microprocessor– Based and Intelligent Systems Engineering, we developed the most powerful mathematical machinery to deal with high–dimensional nonlinear dynamics. In the present text, we consider the extreme cases of nonlinear dynamics, the high–dimensional chaotic and other attractor systems. Although they might look as examples of complete disorder – they still represent control systems, with their inputs, outputs, states, feedbacks, and stability. Today, we can see a number of nice books devoted to nonlinear dyn- ics and chaos theory (see our reference list). However, all these books are only undergraduate, introductory texts, that are concerned exclusively with oversimplified low–dimensional chaos, thus providing only an inspiration for the readers to actually throw themselves into the real–life chaotic dynamics.

Product Details

ISBN-13:	9789048173723
Publisher:	Springer Netherlands
Publication date:	11/19/2010
Series:	Intelligent Systems, Control and Automation: Science and Engineering , #32
Edition description:	Softcover reprint of hardcover 1st ed. 2007
Pages:	697
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

to Attractors and Chaos.- Smale Horseshoes and Homoclinic Dynamics.- 3–Body Problem and Chaos Control.- Phase Transitions and Synergetics.- Phase Synchronization in Chaotic Systems.- Josephson Junctions and Quantum Engineering.- Fractals and Fractional Dynamics.- Turbulence.- Geometry, Solitons and Chaos Field Theory.

Editorial Reviews

From the reviews:

"This is an ambitious book that … is devoted to the understanding, prediction and control of high-dimensional chaotic and attractor systems in real life. … Finally, and most usefully, the book has a substantial list of references (over 30 pages of them), meaning that the book can be used as a guide to literature in a diverse range of topics related to high- (and indeed low-) dimensional chaotic and nonlinear systems." (Peter Ashwin, Mathematical Reviews, Issue 2008 h)

From the Publisher