Department of Physics, College of Sciences, Shiraz University, Shiraz, 71946-84795, Iran.
Department of Physics, Institute for Advanced Studies in Basic sciences (IASBS), Zanjan, 45137-66731, Iran.
Sci Rep. 2017 Aug 2;7(1):7107. doi: 10.1038/s41598-017-07135-6.
Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We therefore consider a simple model of excitable nodes which is known to exhibit a transition to instability at a critical point (λ = 1), and introduce refractory period into its dynamics. We use mean-field analytical calculations as well as numerical simulations to calculate the activity dependent branching ratio that is useful to characterize the behavior of critical systems. We also define avalanches and calculate probability distribution of their size and duration. We find that in the presence of refractory period the dynamics stabilizes while various parameter regimes become accessible. A sub-critical regime with λ < 1.0, a standard critical behavior with exponents close to critical branching process for λ = 1, a regime with 1 < λ < 2 that exhibits an interesting scaling behavior, and an oscillating regime with λ > 2.0. We have therefore shown that refractory behavior leads to a wide range of scaling as well as periodic behavior which are relevant to real neuronal dynamics.
兴奋节点网络最近引起了广泛关注，特别是在神经元动力学方面，有人认为临界性是一个基本属性。被认为是重要动态特性的不应期行为限制了神经元的兴奋性。因此，我们考虑了一个简单的兴奋节点模型，该模型在临界点（λ=1）处表现出不稳定性的转变，并在其动力学中引入不应期。我们使用平均场分析计算以及数值模拟来计算与活动相关的分支比，这有助于描述临界系统的行为。我们还定义了雪崩，并计算了它们大小和持续时间的概率分布。我们发现，在存在不应期的情况下，动力学变得稳定，同时可以访问各种参数范围。存在 1<λ<2 的有趣标度行为的区域，以及具有 λ>2.0 的振荡区域。因此，我们表明不应期行为导致广泛的标度以及与真实神经元动力学相关的周期性行为。
