Overview
- Provides a self-contained introduction to the study of families of slow-fast systems on surfaces
- Contains a unified account of two decades of results on canard cycles
- Presents essential techniques in the study of canard phenomena in a precise and self-contained way
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 73)
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Table of contents (17 chapters)
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Front Matter
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Technical Tools
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Front Matter
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Keywords
About this book
In particular, the book provides a detailed study of the structure of the transitions near the critical set of non-isolated singularities. This leads to precise results on the limit cycles and their bifurcations, including the so-called canard phenomenon and canard explosion. The book also provides a solid basis for the use of asymptotic techniques. It gives a clear understanding of notions like inner and outer solutions, describing their relation and precise structure.
The first part of the book provides a thorough introduction to slow-fast systems, suitable for graduate students. The second and third parts will be of interest to both pure mathematicians working on theoretical questions such as Hilbert's 16th problem, as well as to a wide range of applied mathematicians looking for a detailed understanding of two-scale models found in electrical circuits, population dynamics, ecological models, cellular (FitzHugh–Nagumo) models, epidemiological models, chemical reactions, mechanical oscillators with friction, climate models, and many other models with tipping points.
Authors and Affiliations
About the authors
Freddy Dumortier, born in 1947, emeritus professor at Hasselt University, is former president of the Belgian Mathematical Society and is currently permanent secretary of the Royal Flemish Academy of Belgium for Science and the Arts. He is the author of many papers and his main results deal with singularities and their unfolding, bifurcation theory, Liénard equations, Hilbert's 16th problem, slow-fast systems and the wave speed in reaction-diffusion equations.
Robert Roussarie,born in 1944, is emeritus professor of the University of Bourgogne-Franche Comté. After a career at the CNRS he was professor at the Institut de Mathématique de Bourgogne. He worked on the theory of foliations, of singularities in differential geometry, bifurcations of vector fields and finally slow-fast systems. He also contributed to applied research on ferro-resonance in electrical networks, systems of ecological populations, systems in control theory and free interface problems in combustion theory.
Bibliographic Information
Book Title: Canard Cycles
Book Subtitle: From Birth to Transition
Authors: Peter De Maesschalck, Freddy Dumortier, Robert Roussarie
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-030-79233-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-79232-9Published: 08 August 2021
Softcover ISBN: 978-3-030-79235-0Published: 09 August 2022
eBook ISBN: 978-3-030-79233-6Published: 07 August 2021
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XXI, 408
Number of Illustrations: 59 b/w illustrations, 42 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Analysis, Complexity