Canards Existence in FitzHugh-Nagumo and Hodgkin-Huxley Neuronal Models
Joint Authors
Ginoux, Jean-Marc
Llibre, Jaume
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-12-30
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
In a previous paper we have proposed a new method for proving the existence of “canard solutions” for three- and four-dimensional singularly perturbed systems with only one fast variable which improves the methods used until now.
The aim of this work is to extend this method to the case of four-dimensional singularly perturbed systems with two slow and two fast variables.
This method enables stating a unique generic condition for the existence of “canard solutions” for such four-dimensional singularly perturbed systems which is based on the stability of folded singularities (pseudo singular points in this case) of the normalized slow dynamics deduced from a well-known property of linear algebra.
This unique generic condition is identical to that provided in previous works.
Application of this method to the famous coupled FitzHugh-Nagumo equations and to the Hodgkin-Huxley model enables showing the existence of “canard solutions” in such systems.
American Psychological Association (APA)
Ginoux, Jean-Marc& Llibre, Jaume. 2015. Canards Existence in FitzHugh-Nagumo and Hodgkin-Huxley Neuronal Models. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-17.
https://search.emarefa.net/detail/BIM-1073547
Modern Language Association (MLA)
Ginoux, Jean-Marc& Llibre, Jaume. Canards Existence in FitzHugh-Nagumo and Hodgkin-Huxley Neuronal Models. Mathematical Problems in Engineering No. 2015 (2015), pp.1-17.
https://search.emarefa.net/detail/BIM-1073547
American Medical Association (AMA)
Ginoux, Jean-Marc& Llibre, Jaume. Canards Existence in FitzHugh-Nagumo and Hodgkin-Huxley Neuronal Models. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-17.
https://search.emarefa.net/detail/BIM-1073547
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1073547