Phase Description of Oscillations in Singularly-Perturbed Systems

奇扰动系统中振荡的相描述

基本信息

项目摘要

We want to study the typically irregular oscillations of neuronal activity. For such irregular oscillations, the unsteady rhythm of breathing is a classical example. Using the established method, a simplified description of oscillations builds on their division into characteristic phases. In applications, such a phase description can be used for the detection of very weak interactions between oscillations. However, the standard phase method allows only for a treatment of highly regular oscillations. Therefore, the central goal of our proposal is a sufficient extension of the methods of phase description for an application to realistic neuronal activity, which shows substantial irregularity. In particular, we want to treat two examples of neuronal oscillations. So called noise-induced oscillations (1) exist only in the presence of external fluctuations that arouse the system out of a state that actually does not oscillate. This type of oscillation cannot be described under disregard of the perturbation as it would be tried in the standard phase method. Therefore, another starting point has to be used. For this, we want to extend a recently developed method for the description of breathing. So called bursting (2) is a type of mixed mode oscillation, in a way two oscillators in one, that arises from an interplay of fast and slow time scales. In networks of coupled bursters, the standard phase description breaks down already for weak coupling strength. We, therefore, plan to design a more adequate phase description that achieves a simplified handling of the fast mode by taking an average. In the application to burster networks as they appear in the central nervous system, our goal is to describe the variety of simultaneously occurring synchronization patterns.
我们想研究神经元活动的典型不规则振荡。对于这种不规则的振荡,呼吸的不稳定节奏是一个典型的例子。使用所建立的方法,振荡的简化描述建立在其划分为特征相位的基础上。在应用中,这种相位描述可以用于检测振荡之间的非常弱的相互作用。然而,标准相位法只允许处理高度规则的振荡。因此,我们的建议的中心目标是一个足够的扩展的相位描述的方法的应用到现实的神经元活动,这表明大量的不规则性。 特别是,我们要处理两个例子的神经元振荡。所谓的噪声诱导振荡(1)只存在于外部波动的存在下,这种波动将系统从实际上不振荡的状态中唤醒。这种类型的振荡不能在忽略扰动的情况下描述,因为它将在标准相位法中尝试。因此,必须使用另一个起点。为此,我们想扩展最近开发的呼吸描述方法。所谓的爆发(2)是一种混合模式振荡,在某种程度上是两个振荡器合二为一,它源于快速和慢速时间尺度的相互作用。在耦合突发网络中,标准的相位描述已经因为弱耦合强度而失效。因此,我们计划设计一个更充分的相位描述,通过取平均值来实现快速模式的简化处理。在突发网络出现在中枢神经系统中的应用中,我们的目标是描述各种同时发生的同步模式。

项目成果

期刊论文数量(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Parametric phase diffusion analysis of irregular oscillations
不规则振荡的参数化相扩散分析
  • DOI:
    10.1209/0295-5075/107/68001
  • 发表时间:
    2014
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Justus TC Schwabedal
  • 通讯作者:
    Justus TC Schwabedal
Robust design of polyrhythmic neural circuits.
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Dr. Justus Schwabedal其他文献

Dr. Justus Schwabedal的其他文献

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