论文标题
计算阶段重置曲线的延续方法
A continuation approach to computing phase resetting curves
论文作者
论文摘要
相位重置是研究振荡神经元行为的常见实验方法。假设重复的尖峰或爆发，相位的相位相当于短暂的扰动，导致该周期性运动的阶段发生变化。观察到的效果不仅取决于扰动的强度，还取决于应用扰动的相位。扰动后相变的相位与未扰动的旧相（所谓的相位重置曲线）之间的关系提供了有关神经元行为类型的信息，尽管并不是充分了解扰动性质的所有影响。在本章中，我们介绍了一种基于多段边界值问题的延续，该方法计算ODE模型中的相位重置曲线。我们的方法能够有效地处理系统的相位灵敏度，这意味着它能够处理相位重置曲线的极端变化，包括似乎不连续的重置。我们用两个平面系统的示例说明了算法，我们还展示了相位重置曲线的定性变化如何被表征和理解。一个七维的例子强调，我们的方法不仅限于平面系统，并说明了我们如何处理非瞬时的，时间变化的扰动。
Phase resetting is a common experimental approach to investigating the behaviour of oscillating neurons. Assuming repeated spiking or bursting, a phase reset amounts to a brief perturbation that causes a shift in the phase of this periodic motion. The observed effects not only depend on the strength of the perturbation, but also on the phase at which it is applied. The relationship between the change in phase after the perturbation and the unperturbed old phase, the so-called phase resetting curve, provides information about the type of neuronal behaviour, although not all effects of the nature of the perturbation are well understood. In this chapter, we present a numerical method based on the continuation of a multi-segment boundary value problem that computes phase resetting curves in ODE models. Our method is able to deal effectively with phase sensitivity of a system, meaning that it is able to handle extreme variations in the phase resetting curve, including resets that are seemingly discontinuous. We illustrate the algorithm with two examples of planar systems, where we also demonstrate how qualitative changes of a phase resetting curve can be characterised and understood. A seven-dimensional example emphasises that our method is not restricted to planar systems, and illustrates how we can also deal with non-instantaneous, time-varying perturbations.
