Computation of the response functions of spiral waves in active media
Computation of the response functions of spiral waves in active media
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DOI：
10.1103/physreve.79.056702
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发表时间：
2009-05-01
影响因子：
2.4
通讯作者：
Foulkes, A. J.
中科院分区：
文献类型：
--
作者：
Biktasheva, I. V.;Barkley, D.;Foulkes, A. J.
旋转螺旋波是在物理、化学和生物性质的空间扩展系统中观察到的一种自组织形式。微小的扰动引起螺旋旋转中心的空间位置和频率的逐渐变化，即，漂移螺旋波的响应函数（RF）是对应于临界本征值λ =0，+/- i Ω的伴随线性化算子的本征函数。RF描述了螺旋对小扰动的敏感性，其方式是螺旋对RF接近于零的小扰动不敏感。螺旋漂移的速度与RF与扰动的卷积成比例。在这里，我们开发了一个常规的和通用的方法来计算反应扩散方程中的固定旋转螺旋的RF。我们在FitzHugh-Nagumo系统上证明了该方法，并证明了该方法相对于计算参数的收敛性，即，离散化步骤和介质的大小。所获得的RF被定位在螺旋的核心。
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological natures. A small perturbation causes gradual change in spatial location of spiral's rotation center and frequency, i.e., drift. The response functions (RFs) of a spiral wave are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues lambda=0,+/- i omega. The RFs describe the spiral's sensitivity to small perturbations in the way that a spiral is insensitive to small perturbations where its RFs are close to zero. The velocity of a spiral's drift is proportional to the convolution of RFs with the perturbation. Here we develop a regular and generic method of computing the RFs of stationary rotating spirals in reaction-diffusion equations. We demonstrate the method on the FitzHugh-Nagumo system and also show convergence of the method with respect to the computational parameters, i.e., discretization steps and size of the medium. The obtained RFs are localized at the spiral's core.