Canard Cycles

Canard Cycles
Author :
Publisher : Springer Nature
Total Pages : 408
Release :
ISBN-10 : 9783030792336
ISBN-13 : 3030792331
Rating : 4/5 (331 Downloads)

Book Synopsis Canard Cycles by : Peter De Maesschalck

Download or read book Canard Cycles written by Peter De Maesschalck and published by Springer Nature. This book was released on 2021-08-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Canard Cycles Related Books

Canard Cycles
Language: en
Pages: 408
Authors: Peter De Maesschalck
Categories: Mathematics
Type: BOOK - Published: 2021-08-07 - Publisher: Springer Nature

GET EBOOK

This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are
Canard Cycles and Center Manifolds
Language: en
Pages: 117
Authors: Freddy Dumortier
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: American Mathematical Soc.

GET EBOOK

In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon
Nonautonomous Dynamical Systems in the Life Sciences
Language: en
Pages: 326
Authors: Peter E. Kloeden
Categories: Mathematics
Type: BOOK - Published: 2014-01-22 - Publisher: Springer

GET EBOOK

Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time depend
Geometric Singular Perturbation Theory Beyond the Standard Form
Language: en
Pages: 143
Authors: Martin Wechselberger
Categories: Mathematics
Type: BOOK - Published: 2020-02-21 - Publisher: Springer Nature

GET EBOOK

This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular pert
Mathematical Sciences with Multidisciplinary Applications
Language: en
Pages: 654
Authors: Bourama Toni
Categories: Mathematics
Type: BOOK - Published: 2016-08-19 - Publisher: Springer

GET EBOOK

This book is the fourth in a multidisciplinary series which brings together leading researchers in the STEAM-H disciplines (Science, Technology, Engineering, Ag