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Dynamique et instabilités des filaments de spirales tridimensionnels dans les milieux excitables isotropes

Abstract : Excitable systems are characterized by the existence of a stable equilibrium point and by the fact that the return to equilibrium trajectories can be either simply exponential or long excursions in the phase space depending on the perturbation amplitude. Good approximations of excitable media are simplified reaction-diffusions systems with two variables. Typical examples of excitable media are the heart, the neural axons and the Belousov-Zhabotinsky reaction in gels. In such media the spiral and plane, excitation waves can be observed. This thesis is devoted to the numerical study of the dynamic of possibly twisted scroll waves (spiral waves stacked along a line) in excitable media. First the stationary states are computed using a Newton's method. Second the linear stability of those states is studied, using an iterative method. Then the restabilized states when they exist are determined via direct numerical simulations. The study of untwisted scroll waves shows two kinds of instabilities. The first one corresponds to a Hopf bifurcation and is due to the 3D destabilisation of the meander (periodic variation of the rotation radius of the spiral wave) mode. The restabilized states are studied in detail. the second one, that can be attributed to the destabilisation of the translation mode leads to a disordered state. The study of the influence of twist shows that beyond a critical value of twist, it leads to the destabilisation of the translation modes for finite values of the wavenumber. That instability is a Hopf bifurcation that converts the twist of the scroll wave into Writhe (geometric deformation of the filament). In simple cases the restabilized state is a simple helical filament whereas in more complicated cases, the restabilized state is a stationnary structure that can be seen as the sum of a few helices. An analogy with a twisted elastic rod is presented.
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Contributor : Herve Henry <>
Submitted on : Friday, April 4, 2003 - 2:32:38 PM
Last modification on : Thursday, December 10, 2020 - 12:37:21 PM
Long-term archiving on: : Monday, September 20, 2010 - 12:09:22 PM

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  • HAL Id : tel-00002491, version 2

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Hervé Henry. Dynamique et instabilités des filaments de spirales tridimensionnels dans les milieux excitables isotropes. Biophysique [physics.bio-ph]. Université Paris-Diderot - Paris VII, 2001. Français. ⟨tel-00002491v2⟩

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