Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves.
Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves.
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DOI：
10.1103/physreve.99.022217
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
H. Dierckx;A. Panfilov;H. Verschelde;V. Biktashev;I. Biktasheva
中科院分区：
文献类型：
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作者：
H. Dierckx;A. Panfilov;H. Verschelde;V. Biktashev;I. Biktasheva
在许多振荡或可兴奋系统中，出现的动态模式在移动参考系中是静止的或周期性的。例子包括化学系统或心脏组织中的行波或螺旋波。我们根据扰动和线性算子的伴随临界本征函数（即响应函数）之间的重叠积分，提出了一个统一的理论框架，用于在小外部扰动下此类模式的漂移。对于螺旋波，考虑了螺旋尖端轨迹的有限半径和螺旋波曲折。可以选择不同的坐标系，具体取决于是否想要预测螺旋波尖端的运动、时间平均尖端路径或蜿蜒花的中心。该框架用于分析不同状态下恒定外场中蜿蜒螺旋波的漂移。
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.