Phase-Amplitude Descriptions of Neural Oscillator Models
Phase-Amplitude Descriptions of Neural Oscillator Models
复制标题
神经振荡器模型的相位-幅度描述
DOI：
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发表时间：
2013
影响因子：
2.3
通讯作者：
S. Coombes
中科院分区：
文献类型：
--
作者：
K. Wedgwood;Kevin K. Lin;R. Thul;S. Coombes
对于许多表现出强吸引极限环的单神经元模型的简化描述，相位振子是一个常见的起点。分析这类模型对弱扰动的响应的框架现在特别先进，并允许弱连接神经网络理论的发展。然而，对于许多神经振荡器模型来说，强吸引假设可能并不是自然的假设。例如，众所周知，流行的基于电导的Morris-LeCar模型以一种混沌的方式对周期性脉动刺激做出响应，而这种方式不能用相位减少来充分描述。在这篇文章中，我们推广了相位描述，它允许人们跟踪从周期到周期的距离的演变以及周期上的相位。我们使用了常微分方程组理论中的一种经典方法，即利用移动坐标系来分析周期轨道。随后的相位-幅度描述被证明非常适合于理解振荡器对外部刺激(不一定弱)的响应。我们考虑了一些神经振子模型的例子，从平面到高维模型，来说明这种方法在提供对标准相位减少技术的改进方面的有效性。作为这一相位-振幅框架的一个显式应用，我们较详细地考虑了强吸引假设不成立的一般平面模型的响应，并考察了系统对周期脉动强迫的响应。此外，我们还探讨了动态剪切的存在如何导致混沌响应。
Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris–Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.
影响因子：
1.9
作者：
KEPLER, TB;ABBOTT, LF;MARDER, E
通讯作者：
MARDER, E