Stability of periodic traveling waves in the Aliev-Panfilov reaction-diffusion system
Stability of periodic traveling waves in the Aliev-Panfilov reaction-diffusion system
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DOI：
10.1016/j.cnsns.2015.09.002
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发表时间：
2016-04-01
影响因子：
3.9
通讯作者：
Ogawa, Toshiyuki
中科院分区：
文献类型：
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作者：
Gani, M. Osman;Ogawa, Toshiyuki
本文研究了心脏兴奋的二分量Aliev-Panfilov反应扩散系统。据了解，该模型在二维空间域中表现出螺旋波不稳定性。为了描述螺旋波不稳定性，重要的是要了解周期行波不稳定性所产生的模型。我们确定了该模型中周期行波的存在性和稳定性。此外，我们还计算了二维参数平面中稳定和不稳定周期行波之间的稳定边界。观察到周期行波通过Eckhaus型的稳定性变化来表示不稳定性。结果，稳定波分叉为振荡周期行波。我们通过计算波的基本谱来描述这些现象。此外，我们研究了作为两个零倾之间的间隙的函数的波的稳定性。在二维情况下，我们根据周期行波的稳定性边界确定了螺旋波的不稳定性。(C)2015 Elsevier B. V.版权所有。
We study the two-component Aliev-Panfilov reaction-diffusion system of cardiac excitation. It is known that the model exhibits spiral wave instability in two-dimensional spatial domains. In order to describe the spiral wave instability, it is important to understand periodic traveling wave instability resulting from the model. We determine the existence and stability of periodic traveling waves in the model. In addition, we calculate the stability boundary between stable and unstable periodic traveling waves in a two-dimensional parameter plane. It is observed that the periodic traveling waves express instability by a stability change of Eckhaus type. As a result, a stable wave bifurcates to an oscillating periodic traveling wave. We describe these phenomena by calculating the essential spectra of the waves. Furthermore, we study the stability of the waves as a function of the gaps between two nullclines. In two dimensions, we determine the spiral wave instability based on the stability boundary of the periodic traveling waves. (C) 2015 Elsevier B.V. All rights reserved.