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Noise-Induced Transitions

Theory and Applications in Physics, Chemistry, and Biology

  • Book
  • © 1984

Overview

Authors:
  1. Werner Horsthemke

    1. Southern Methodist University, Dallas, USA

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  2. René Lefever

    1. Université Libre de Bruxelles, Brussels, Belgium

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Series in Synergetics (SSSYN, volume 15)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction

    Pages 1-22

  3. Elements of Probability Theory

    Pages 23-54

  4. Stochastic Models of Environmental Fluctuations

    Pages 55-64

  5. Markovian Diffusion Processes

    Pages 65-81

  6. Stochastic Differential Equations

    Pages 82-107

  7. Noise-Induced Nonequilibrium Phase Transitions

    Pages 108-163

  8. Noise-Induced Transitions in Physics, Chemistry, and Biology

    Pages 164-200

  9. External Colored Noise

    Pages 201-257

  10. Markovian Dichotomous Noise: An Exactly Soluble Colored-Noise Case

    Pages 258-292

  11. The Symbiosis of Noise and Order — Concluding Remarks

    Pages 293-294

  12. Back Matter

    Pages 295-318
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Keywords

About this book

The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during the last two decades. The behavior of far from equilibrium systems has received more and more attention and has been an extremely active and productive subject of research for physicists, chemists and biologists. Their studies have brought about a more unified vision of the laws which govern self-organization processes of physico-chemical and biological sys­ tems. A major achievement has been the extension of the notion of phase transi­ tion to instabilities which occur only in open nonlinear systems. The notion of phase transition has been proven fruitful in apphcation to nonequilibrium ins- bihties known for about eight decades, like certain hydrodynamic instabilities, as well as in the case of the more recently discovered instabilities in quantum optical systems such as the laser, in chemical systems such as the Belousov-Zhabotinskii reaction and in biological systems. Even outside the realm of natural sciences, this notion is now used in economics and sociology. In this monograph we show that the notion of phase transition can be extend­ ed even further. It apphes also to a new class of transition phenomena which occur only in nonequilibrium systems subjected to a randomly fluctuating en­ vironment.

Authors and Affiliations

  • Southern Methodist University, Dallas, USA

    Werner Horsthemke

  • Université Libre de Bruxelles, Brussels, Belgium

    René Lefever

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