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| The phase response curve (PRC) is a powerful tool to study the effect of a perturbation on the phase of an oscillator, assuming that the dynamics can be explained by the phase variable. However, factors like the rate of convergence to the oscillator or high stimulation frequency may invalidate this assumption and raise the question of how is the phase variation away from an attractor. Then the concept of isochron turns out to be crucial; from it, we propose an extension of advancement functions to the transient states by defining the Phase Response Functions (PRF) and the Amplitude Response Function (ARF). Using these we study the case of a pulse-train periodic 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. Apart from the comparison between 1D and 2D predictions, we also pay attention to bifurcations in the 2D maps that do not occur when using 1D maps. 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. |
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