Theory of spiral wave dynamics in weakly excitable media: Asymptotic reduction to a kinematic model and applications

被引:101
作者
Hakim, V
Karma, A
机构
[1] Ecole Normale Super, Phys Stat Lab, CNRS, F-75231 Paris 05, France
[2] Univ Paris 06, Phys Stat Lab, F-75231 Paris, France
[3] Univ Paris 07, Phys Stat Lab, Paris, France
[4] Northeastern Univ, Dept Phys, Boston, MA 02115 USA
[5] Northeastern Univ, Ctr Interdisciliniary Res Complex Syst, Boston, MA 02115 USA
来源
PHYSICAL REVIEW E | 1999年 / 60卷 / 05期
关键词
D O I
10.1103/PhysRevE.60.5073
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract, causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wave front, slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency, (iii) drift under external actions (external field .with application to axisymmetric scroll ring motion in three dimensions, and spatial-or/and time-dependent variation of excitability), and (iv) the dynamics of multiarmed spiral waves with the prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHugh-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semiquantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models. [S1063-651X(99)01610-4].
引用
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页码:5073 / 5105
页数:33
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