多脉冲相位复位曲线
Multi-pulse phase resetting curve
摘要：
本文从相位响应曲线（PRC）的角度出发，系统地研究了双脉冲激励对自振子动力学特性的影响。具体来说，我们测试的偏差从两个小扰动的相位提前的线性总和。我们推导出解析的校正项，它通常出现在振荡器的固有维数大于一。我们证明了这种效果的情况下的Stuart-Landau模型，也在各种高维神经元模型。发现非线性校正与扰动的平方成正比。在研究脉冲耦合振荡器网络时，需要考虑这种偏离叠加原理的情况。此外，该偏差可以用于经由双脉冲激励来验证振荡器模型。
英文摘要：
In this paper, we introduce and systematically study, in terms of phase response curves (PRC), the effect of a dual pulse excitation on the dynamics of an autonomous oscillator. Specifically, we test the deviations from a linear summation of phase advances from two small perturbations. We derive analytically a correction term, which generally appears for oscillators whose intrinsic dimensionality is greater than one. We demonstrate this effect in case of the Stuart-Landau model, and also in various higher dimensional neuronal model. The non-linear correction is found to be proportional to the square of the perturbation. This deviation from the superposition principle needs to be taken into account in studies of networks of pulse-coupled oscillators. Further, this deviation could be used for verification of oscillator models via a dual pulse excitation.
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