The FitzHugh-Nagumo Model: Bifurcation and Dynamics / Edition 1

The FitzHugh-Nagumo Model: Bifurcation and Dynamics / Edition 1

by C. Rocsoreanu, A. Georgescu, N. Giurgiteanu, N. Giurgiwteanu
     
 

ISBN-10: 0792364279

ISBN-13: 9780792364276

Pub. Date: 08/31/2000

Publisher: Springer Netherlands

This application-oriented monograph presents a comprehensive theoretical and numerical investigation of all types of oscillators and bifurcations (such as Hopf, Bogdanov-Takens, Bautin, and homoclinic) generated by the FitzHugh-Nagumo model. The wide diversity of the oscillators as used in electrophysiology, biology, and engineering is emphasised. Various

Overview

This application-oriented monograph presents a comprehensive theoretical and numerical investigation of all types of oscillators and bifurcations (such as Hopf, Bogdanov-Takens, Bautin, and homoclinic) generated by the FitzHugh-Nagumo model. The wide diversity of the oscillators as used in electrophysiology, biology, and engineering is emphasised. Various asymptotic behaviours are revealed. The dramatic changes in oscillations connected with the emergence or disappearance of concave limit cycles are investigated. Codimension of bifurcations is minutely analysed. New types of codimension one and two bifurcations of planar systems were found. A detailed global bifurcation diagram concludes the work.
Audience: This volume will be of interest to researchers and graduate students whose work involves the mathematics of biology, ordinary differential equations, approximations and expansions, cardiac electrophysiology, biological transport, and cell membranes.

Product Details

ISBN-13:
9780792364276
Publisher:
Springer Netherlands
Publication date:
08/31/2000
Series:
Mathematical Modelling: Theory and Applications Series, #10
Edition description:
2000
Pages:
249
Product dimensions:
6.14(w) x 9.21(h) x 0.24(d)

Table of Contents

Introduction. 1. Models and Dynamics. 2. Static Bifurcation and Linearization of the Fitzhugh-Nagumo Model. 3. Dynamic Bifurcation for the Fitzhugh-Nagumo Model. 4. Models of Asymptotic Approximation for the Fitzhugh-Nagumo System as c --> ? 5. Global Bifurcation Diagram and Phase Dynamics for the Fitzhugh-Nagumo Model. References. Index.

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