High-Dimensional Chaotic and Attractor Systems A Comprehensive Introduction [Paperback]

This graduatelevel textbook is devoted to understanding, prediction and control of highdimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in highdimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincar?s 3-body problem, high-tech Josephson junctions, and more.

If we try to describe real world in mathematical terms, we will see that real life is very often a highdimensional 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 highdimensional 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 highdimensional nonlinear dynamics. In the present text, we consider the extreme cases of nonlinear dynamics, the highdimensional 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 oversimpli?ed lowdimensional chaos, thus providing only an inspiration for the readers to actually throw themselves into the reallife chaotic dynamics.1. Introduction to Attractors and Chaos1.1 Basics of Attractor and Chaotic Dynamics1.2 Brief History of Chaos TheorylC†