噪声和分岔结构对混合模振荡的影响
Characterizing mixed mode oscillations shaped by noise and bifurcation structure
摘要：
许多神经元系统和模型显示出某种类型的混合模式振荡（MMO），由散布着尖峰的小振幅振荡周期组成。已经提出了具有不同底层机制的各种模型来生成这种类型的行为。这些模型的随机版本可以产生类似的时间序列，通常具有与确定性模型不同的噪声驱动机制。我们提出了一套措施，当应用到时间序列，用于区分模型和分类路线生产MMO，如噪声引起的振荡或延迟分叉。通过聚焦于阈下振荡，我们分析了峰间间隔密度、振幅趋势和相干性度量。我们开发这些措施的生物物理模型星状细胞和现象学FitzHugh-Nagumo型模型，并将其应用于相关模型。分析突出了一种新的方法，使用噪声水平来区分模型类型和MMO机制的背景下，模型参数和复位和返回机制的影响。最后，我们指出如何可以应用到实验时间序列的措施，揭示潜在的动力学结构，同时利用系统的固有噪声或可调的外部噪声。
英文摘要：
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and reset and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.
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