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High-Dimensional Chaotic and Attractor Systems

A Comprehensive Introduction

  • Book
  • © 2007

Overview

Authors:
  1. Vladimir G. Ivancevic

    1. Defence Science and Technology Organisation, Adelaide, Australia

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    You can also search for this author in PubMed   Google Scholar

  2. Tijana T. Ivancevic

    1. The University of Adelaide, Australia

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    You can also search for this author in PubMed   Google Scholar

  • High-dimensional chaos of real life
  • Real research – not motivational introduction

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction to Attractors and Chaos

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 1-151

  3. Smale Horseshoes and Homoclinic Dynamics

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 153-222

  4. 3–Body Problem and Chaos Control

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 223-284

  5. Phase Transitions and Synergetics

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 285-418

  6. Phase Synchronization in Chaotic Systems

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 419-455

  7. Josephson Junctions and Quantum Engineering

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 457-489

  8. Fractals and Fractional Dynamics

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 491-527

  9. Turbulence

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 529-616

  10. Geometry, Solitons and Chaos Field Theory

    • Vladimir G. Ivancevic, Tijana T. Ivancevic
    Pages 617-651

  11. Back Matter

    Pages 653-702
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Defence Science and Technology Organisation, Adelaide, Australia

    Vladimir G. Ivancevic

  • The University of Adelaide, Australia

    Tijana T. Ivancevic

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