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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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The Fitzhugh-Nagumo Model: Bifurcation and Dynamics

The Fitzhugh-Nagumo Model: Bifurcation and Dynamics

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

Paperback

Series: Mathematical Modelling: Theory and Applications, Book 10

Medical ReferenceGeneral Mathematics

ISBN10: 9048155126
ISBN13: 9789048155125
Publisher: Springer Nature
Published: Dec 8 2010
Pages: 238
Weight: 0.79
Height: 0.53 Width: 6.14 Depth: 9.21
Language: English
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.

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