High-Dimensional Chaotic and Attractor Systems - Ivancevic, Tijana T.

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Résumé :
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 oversimpli?ed low?dimensional chaos, thus providing only an inspiration for the readers to actually throw themselves into the real?life chaotic dynamics.

Sommaire:
This book details prediction and control of high-dimensional chaotic and attractor systems of real life. It provides a scientific tool that will enable the actual performance of competitive research in high-dimensional chaotic and attractor dynamics. Coverage details Smale's topological transformations of stretching, squeezing and folding and Poincar?'s 3-body problem and basic techniques of chaos control. It offers a review of both Landau's and topological phase transition theory as well as Haken's synergetics and deals with phase synchronization in high-dimensional chaotic systems. In addition, the book presents high-tech Josephson junctions, deals with fractals and fractional Hamiltonian dynamics, and offers a review of modern techniques for dealing with turbulence. It also offers a brief on the cutting edge techniques of the high-dimensional nonlinear dynamics (including geometries, gauges and solitons, culminating into the chaos field theory)....