The phase response curve (PRC) is a powerful tool to study the effect of a perturbation on the phase of an oscillator, assuming that all the dynamics can be explained by the phase variable. However, factors like the rate of convergence to the oscillator, strong forcing or high stimulation frequency may invalidate the above assumption and raise the question of how is the phase variation away from an attractor. The concept of isochrons turns out to be crucial to answer this question; from it, we have built up Phase Response Functions (PRF) and, in the present paper, we complete the extension of advancement functions to the transient states by defining the Amplitude Response Function (ARF) to control changes in the transversal variables. Based on the knowledge of both the PRF and the ARF, we study the case of a pulse-train stimulus, and compare the predictions given by the PRC-approach (a 1D map) to those given by the PRF-ARF-approach (a 2D map); we observe differences up to two orders of magnitude in favor of the 2D predictions, especially when the stimulation frequency is high or the strength of the stimulus is large. We also explore the role of hyperbolicity of the limit cycle as well as geometric aspects of the isochrons. Summing up, we aim at enlightening the contribution of transient effects in predicting the phase response and showing the limits of the phase reduction approach to prevent from falling into wrong predictions in synchronization problems. LIST OF ABBREVIATIONS PRC phase response curve, phase resetting curve.PRF phase response function.ARF amplitude response function.

中文翻译：

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瞬态刺激的相位幅度响应函数。

相位响应曲线 (PRC) 是研究扰动对振荡器相位影响的有力工具，假设所有动力学都可以用相位变量来解释。然而，振荡器的收敛速度、强强迫或高刺激频率等因素可能会使上述假设无效，并提出相位变化如何远离吸引子的问题。事实证明，等时线的概念对于回答这个问题至关重要。从中，我们建立了相位响应函数（PRF），并且在本文中，我们通过定义幅度响应函数（ARF）来控制横向变量的变化，完成了推进函数到瞬态的扩展。基于 PRF 和 ARF 的知识，我们研究了脉冲序列刺激的情况，并将PRC方法（一维地图）给出的预测与PRF-ARF方法（二维地图）给出的预测进行比较；我们观察到两个数量级的差异有利于二维预测，尤其是当刺激频率很高或刺激强度很大时。我们还探讨了极限环的双曲线的作用以及等时线的几何方面。总而言之，我们旨在启发瞬态效应在预测相位响应中的贡献，并展示相位减少方法的局限性，以防止在同步问题中陷入错误预测。缩略语列表 PRC 相位响应曲线、相位复位曲线。PRF 相位响应函数。ARF 幅值响应函数。