Asymptotic behavior of fronts and pulses of the bidomain model
The bidomain model is the standard model for cardiac electrophysiology. In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of the bidomain Allen-Cahn equation and the bidomain FitzHugh-Nagumo equation in two spatial dimension. In previous work, i...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
01.05.2021
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Subjects | |
Online Access | Get full text |
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Summary: | The bidomain model is the standard model for cardiac electrophysiology. In
this paper, we investigate the instability and asymptotic behavior of planar
fronts and planar pulses of the bidomain Allen-Cahn equation and the bidomain
FitzHugh-Nagumo equation in two spatial dimension. In previous work, it was
shown that planar fronts of the bidomain Allen-Cahn equation can become
unstable in contrast to the classical Allen-Cahn equation. We find that, after
the planar front is destabilized, a rotating zigzag front develops whose shape
can be explained by simple geometric arguments using a suitable Frank diagram.
We also show that the Hopf bifurcation through which the front becomes unstable
can be either supercritical or subcritical, by demonstrating a parameter regime
in which a stable planar front and zigzag front can coexist. In our
computational studies of the bidomain FitzHugh-Nagumo pulse solution, we show
that the pulses can also become unstable much like the bidomain Allen-Cahn
fronts. However, unlike the bidomain Allen-Cahn case, the destabilized pulse
does not necessarily develop into a zigzag pulse. For certain choice of
parameters, the destabilized pulse can disintegrate entirely. These studies are
made possible by the development of a numerical scheme that allows for the
accurate computation of the bidomain equation in a two dimensional strip domain
of infinite extent. |
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Bibliography: | RIKEN-iTHEMS-Report-21 |
DOI: | 10.48550/arxiv.2105.00169 |