Franović Igor, Omel'chenko Oleh E, Wolfrum Matthias
Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany.
Chaos. 2018 Jul;28(7):071105. doi: 10.1063/1.5045179.
The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e., the excitability happens to be phase-sensitive. As a paradigmatic example of this concept, we employ the classical FitzHugh-Nagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase-sensitive nonlinear threshold-like response to perturbations, which can be explained by the nonlinear behavior in the vicinity of the canard trajectory. Triggering the phase-sensitive excitability of the relaxation oscillations by noise, we find a characteristic non-monotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this non-monotone dependence as a result of an interplay of two competing effects of the increasing noise: the growing efficiency of the excitation and the degradation of the nonlinear response.
兴奋性的经典概念指的是一种平衡状态，在扰动影响下呈现出非线性阈值样行为。在此，我们通过展示周期性轨道如何能展现出一种特定形式的可激发行为来扩展这一概念，其中非线性阈值样响应仅在周期性轨道的特定部分施加扰动后才出现，即兴奋性是相位敏感的。作为这一概念的一个典型例子，我们采用经典的菲茨休 - 纳古莫系统。出现在该系统振荡区域的弛豫振荡，结果显示出对扰动的相位敏感非线性阈值样响应，这可以通过鸭轨道附近的非线性行为来解释。通过噪声触发弛豫振荡的相位敏感兴奋性，我们发现弛豫振荡的平均尖峰率对噪声水平呈现出特征性的非单调依赖关系。我们将这种非单调依赖关系解释为噪声增加的两种竞争效应相互作用的结果：激发效率的提高和非线性响应的退化。
