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The FitzHugh-Nagumo Model

Bifurcation and Dynamics

  • Book
  • © 2000

Overview

Authors:
  1. C. Rocşoreanu

    1. Department of Mathematics, University of Craiova, Craiova, Romania

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  2. A. Georgescu

    1. Department of Mathematics, University of Piteşti, Piteşti, Romania

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    You can also search for this author in PubMed   Google Scholar

  3. N. Giurgiţeanu

    1. Department of Economics, University of Craiova, Craiova, Romania

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Part of the book series: Mathematical Modelling: Theory and Applications (MMTA, volume 10)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
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  2. Models and Dynamics

    • C. Rocşoreanu, A. Georgescu, N. Giurgiţeanu
    Pages 1-52

  3. Static Bifurcation and Linearization of the FitzHugh-Nagumo Model

    • C. Rocşoreanu, A. Georgescu, N. Giurgiţeanu
    Pages 53-95

  4. Dynamic Bifurcation for the FitzHugh-Nagumo Model

    • C. Rocşoreanu, A. Georgescu, N. Giurgiţeanu
    Pages 97-148

  5. Models of Asymptotic Approximation for the FitzHugh-Nagumo System as c → ∞

    • C. Rocşoreanu, A. Georgescu, N. Giurgiţeanu
    Pages 149-177

  6. Global Bifurcation Diagram and Phase Dynamics for the FitzHugh-Nagumo Model

    • C. Rocşoreanu, A. Georgescu, N. Giurgiţeanu
    Pages 179-219

  7. Back Matter

    Pages 221-236
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Craiova, Craiova, Romania

    C. Rocşoreanu

  • Department of Mathematics, University of Piteşti, Piteşti, Romania

    A. Georgescu

  • Department of Economics, University of Craiova, Craiova, Romania

    N. Giurgiţeanu

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