C Rocsoreanu

(Author)

The Fitzhugh-Nagumo Model: Bifurcation and DynamicsPaperback, 8 December 2010

The Fitzhugh-Nagumo Model: Bifurcation and Dynamics
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Part of Series
Mathematical Modelling: Theory and Applications
Print Length
238 pages
Language
English
Publisher
Springer
Date Published
8 Dec 2010
ISBN-10
9048155126
ISBN-13
9789048155125

Description

The present monograph analyses the FitzHugh-Nagumo (F-N) model Le., the Cauchy problem for some generalized Van der Pol equation depending on three real parameters a, band c. This model, given in (1. 1. 17), governs the initiation of the cardiac impulse. The presence of the three parameters leads to a large variety of dy- namics, each of them responsible for a specific functioning of the heart. For physiologists it is highly desirable to have aglobai view of all possible qualitatively distinct responses of the F-N model for all values of the pa- rameters. This reduces to the knowledge of the global bifurcation diagram. So far, only a few partial results appeared and they were spread through- out the literature. Our work provides a more or less complete theoretical and numerical investigation of the complex phase dynamics and bifurca- tions associated with the F-N dynamical system. This study includes the static and dynamic bifurcations generated by the variation of a, band c and the corresponding oscillations, of special interest for applications. It enables one to predict all possible types of initiations of heart beats and the mechanism of transformation of some types of oscillations into others by following the dynamics along transient phase space trajectories. Of course, all these results hold for the F-N model. The global phase space picture enables one to determine the domain of validity of this model.

Product Details

Authors:
C RocsoreanuA GeorgescuN Giurgiteanu
Book Format:
Paperback
Country of Origin:
NL
Date Published:
8 December 2010
Dimensions:
23.39 x 15.6 x 1.35 cm
ISBN-10:
9048155126
ISBN-13:
9789048155125
Language:
English
Location:
Dordrecht
Pages:
238
Publisher:
Weight:
358.34 gm

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