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Singular Perturbations and HysteresisSingular Perturbations and Hysteresis

Michael P. Mortell, Robert E. O'Malley, Alexei Pokrovskii, and Vladimir Sobolev, Editors

This book brings together many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and reasonably comprehensive fashion. To bridge a gap between practitioners of these phenomena, the editors conducted a workshop in April 2002 at University College Cork to provide a forum for experts in both fields to share their interests and knowledge. For this book, the editors have compiled research from those practitioners in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modeling, and fluid mechanics, all with an emphasis on hysteresis and singular perturbations.

The book begins with a basic introduction to hysteresis and singular perturbations theory, including simple examples from both physics and mathematics. Later chapters address

  • applications of hysteresis to economics,
  • various aspects of the asymptotic theory of singularly perturbed systems,
  • typical problems of the asymptotic theory of contrast structures, and
  • the geometrical approach to an investigation of models with singular perturbations and hysteresis.

The editors intend for this text not only to be a useful and accessible introduction to techniques and the research literature but also to generate new ideas for researchers and to attract new researchers into this vibrant and dynamic field.


This is a book for applied mathematicians, engineers, and physicists curious about the important nonlinear phenomena of singular perturbations and hysteresis.


List of Contributors; Preface; Chapter 1: A Naïve View of Time Relaxation and Hysteresis, A. Pokrovskii, V. Sobolev; Chapter 2: Frustration Minimization, Hysteresis and the El Farol Problem, R. Cross, M. Grinfeld, H. Lamba, A. Pittock; Chapter 3: Hysteresis in Singularly Perturbed Problems, P. Krejčí; Chapter 4: Combined Asymptotic Expansions, E. Benoît, A. Fruchard, A. El Hamidi; Chapter 5: Contrast Structures of Alternating Type, A. Vasilieva; Chapter 6: Multi-Dimensional Internal Layers, N. Nefedov; Chapter 7: Geometry of Singular Perturbations: Critical Cases, V. Sobolev; Chapter 8: Black Swans and Canards in Laser and Combustion Models, E. Shchepakina, V. Sobolev; Chapter 9: Multi-Scale Analysis of Pressure Driven Flames, V. Bykov, I. Goldfarb, V. Gol’dshtein; Chapter 10: Split-Hyperbolicity, Hysteresis and Lang-Kobayashi Equations, A. Pokrovskii, O. Rasskazov, R. Studdert; Index.

2005 / 360 pages / Softcover / ISBN-13: 978-0-898715-97-2 / ISBN-10: 0-89871-597-0 /
List Price $74.00 / SIAM Member Price $51.80 / Order Code OT95
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