用响应函数计算螺旋波的漂移速度
Computation of the Drift Velocity of Spiral Waves using Response Functions
摘要：
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。在存在小扰动的情况下，螺旋波的旋转中心和基准相位可以随时间改变，即螺旋波漂移。在线性近似中，漂移的速度与扰动与螺旋响应函数（RF）的卷积成比例，RF是对应于临界本征值$λ= 0, \pm iω$的伴随线性化算子的本征函数。在这里，我们证明了响应函数给出定量准确的预测的漂移速度由于各种扰动：一个依赖于时间的，周期性的扰动（诱导共振漂移）;一个旋转对称性破坏扰动（诱导电泳漂移）;和一个平移对称性破坏扰动（不均匀性诱导漂移），包括漂移由于梯度，逐步和本地化的不均匀性。我们预测的漂移速度使用的响应函数在FitzHugh-Nagumo（FHN）和巴克利模型，并将它们与直接数值模拟中获得的速度。在所有情况下，良好的定量协议证明。
英文摘要：
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave's centre 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 (RFs), which are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues $λ= 0, \pm iω$. 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, step-wise and localised inhomogeneity. We predict the drift velocities using the response functions in FitzHugh-Nagumo (FHN) and Barkley models, and compare them with the velocities obtained in direct numerical simulations. In all cases good quantitative agreement is demonstrated.
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