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Probability and Its Applications
cover

Noise-Induced Phenomena in Slow-Fast Dynamical Systems

A Sample-Paths Approach

Authors: Berglund, Nils, Gentz, Barbara

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About this book

Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation theory, allows the domains of concentration for typical sample paths to be determined, and provides precise estimates on the transition probabilities between these domains.

In addition to the detailed presentation of the set-up and mathematical results, applications to problems in physics, biology, and climatology are discussed. The emphasis lies on noise-induced phenomena such as stochastic resonance, hysteresis, excitability, and the reduction of bifurcation delay.

Nils Berglund joined the research group "Classical and Quantum Dynamics" at the Centre de Physique Théorique (CNRS) in Marseille-Luminy in 2001. He teaches in the Mathematics Department of the Université du Sud Toulon-Var.

Barbara Gentz joined the research group "Interacting Random Systems" at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) in Berlin in 1998. She teaches in the Institute of Mathematics at the Technical University in Berlin.

 

Reviews

From the reviews:

"This well-written book presents an approach based on a series of articles of both authors. The main aim is a characterisation of typical sample paths for slow-fast systems. Presenting a detailed exposition of the setup and mathematical results, as well as a path to recent applied research, the book is aimed at a wide range of readers, from advanced students to researchers in mathematics, physics, or engineering." (Dirk Blömker, Mathematical Reviews, Issue 2007 b)


Table of contents (6 chapters)

Table of contents (6 chapters)
  • Introduction

    Pages 1-16

  • Deterministic Slow-Fast Systems

    Pages 17-49

  • One-Dimensional Slowly Time-Dependent Systems

    Pages 51-110

  • Stochastic Resonance

    Pages 111-142

  • Multi-Dimensional Slow-Fast Systems

    Pages 143-191

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-1-84628-186-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-1-84628-038-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA in USD
  • ISBN 978-1-84996-547-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Noise-Induced Phenomena in Slow-Fast Dynamical Systems
Book Subtitle
A Sample-Paths Approach
Authors
Series Title
Probability and Its Applications
Copyright
2006
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84628-186-0
DOI
10.1007/1-84628-186-5
Hardcover ISBN
978-1-84628-038-2
Softcover ISBN
978-1-84996-547-7
Series ISSN
1431-7028
Edition Number
1
Number of Pages
XIII, 276
Number of Illustrations
57 b/w illustrations
Topics

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