http://pre.aps.org/abstract/PRE/v81/i6/e066202
Computation of the drift velocity of spiral waves using response functions
Abstract: Rotating spiral waves are a form of self-organization observed in spatially extended systems of chysical,chemical, and biological nature. In the presence of a small perturbation, the spiral wave’s center of rotation and fiducial phase may change over time, i.e., the spiral wave drifts. In linear approximation, the velocity of the
drift is proportional to the convolution of the perturbation with the spiral’s response functions, which are the
eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues =0, +-omega. Here, we
demonstrate that the response functions give quantitatively accurate prediction of the drift velocities due to a
variety of perturbations: a time dependent, periodic perturbation inducing resonant drift; a rotational
symmetry-breaking perturbation inducing electrophoretic drift; and a translational symmetry-breaking perturbation
inhomogeneity induced drift including drift due to a gradient, stepwise, and localized inhomogeneity.
We predict the drift velocities using the response functions in FitzHugh-Nagumo and Barkley models,
and compare them with the velocities obtained in direct numerical simulations. In all cases good quantitative
agreement is demonstrated.
这是作者所在研究组一系列文章的一个总结类文献，理论基石仍然是第二作者，D. Barkley在上世纪九十年代发展的稳定性分析。
如其所言，计算response 函数的复杂性让一般，习惯于直接模拟的研究者有点发怵，别人我不敢说，对于我是这样的。
我感兴趣的是其中的“resonant drift”.
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