High-Dimensional Chaotic and Attractor Systems

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.