Peter de Maesschalck

(Author)

Canard Cycles: From Birth to Transition (2021)Paperback - 2021, 9 August 2022

Canard Cycles: From Birth to Transition (2021)
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Part of Series
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge /
Print Length
408 pages
Language
English
Publisher
Springer
Date Published
9 Aug 2022
ISBN-10
3030792358
ISBN-13
9783030792350

Description

This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are treated in the general context of slow-fast families of two-dimensional vector fields. The central question of controlling the limit cycles is addressed in detail and strong results are presented with complete proofs.
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.

Product Details

Authors:
Peter de MaesschalckFreddy DumortierRobert Roussarie
Book Edition:
2021
Book Format:
Paperback
Country of Origin:
NL
Date Published:
9 August 2022
Dimensions:
23.39 x 15.6 x 2.24 cm
ISBN-10:
3030792358
ISBN-13:
9783030792350
Language:
English
Location:
Cham
Pages:
408
Publisher:
Weight:
603.28 gm

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