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From Instability to Intelligence

Complexity and Predictability in Nonlinear Dynamics

  • Book
  • © 1997

Overview

Authors:
  1. Michail Zak

    1. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA

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  2. Joseph P. Zbilut

    1. Department of Molecular Biophysics and Physiology, Rush University, Chicago, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Ronald E. Meyers

    1. US Army Research Laboratory, Adelphi, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 49)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Introduction

    1. Introduction

      Pages 1-7

  3. Predictability in Classical Dynamics

    1. Front Matter

      Pages 9-9
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    2. Open Problems in Dynamical Systems

      Pages 11-53

    3. Instability in Dynamics

      Pages 55-131

    4. Stabilization Principle

      Pages 133-238

  5. Back Matter

    Pages 529-552
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Keywords

About this book

So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some­ thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi­ bility in thermodynamics, the phenomena of chaos and turbulence in clas­ sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de­ scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al­ ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.

Authors and Affiliations

  • Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USA

    Michail Zak

  • Department of Molecular Biophysics and Physiology, Rush University, Chicago, USA

    Joseph P. Zbilut

  • US Army Research Laboratory, Adelphi, USA

    Ronald E. Meyers

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