论文标题
与惯性
Intermittent chaotic spiking in the van der Pol-FitzHugh-Nagumo system with inertia
论文作者
论文摘要
显示出具有惯性的三维（3D）Fitzhugh-Nagumo神经元模型，显示出由大振幅尖峰组成的混沌混合模式动力学，该动力学由大量的小振幅混乱振荡分开。与由噪声驱动的标准2D Fitzhugh-Nagumo模型相反，尖刺间隔分布显示了与混沌吸引子的不稳定周期轨道相关的尖峰的复杂排列。对于控制系统兴奋性的许多参数范围，我们观察到混乱的混合模式状态由其他高度不规则的尖峰交织的几乎正常尖峰的失误组成。我们在这里探索这些结构的出现，并显示它们与间歇性过渡到混乱的对应关系。实际上，比在鞍节节点分叉附近的动态系统I型在I型I型Intermittilence上的平均射击状态下的平均停留时间（作为控制参数的函数）遵守相同的缩放定律。我们假设这种情况也存在于多种慢速神经元模型中，这些模型的特征是二维快速流形和一维慢的神经元模型。
The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast to the standard 2D Fitzhugh-Nagumo model driven by noise, the interspike-intervals distribution displays a complex arrangement of sharp peaks related to the unstable periodic orbits of the chaotic attractor. For many ranges of parameters controlling the excitability of the system, we observe that chaotic mixed-mode states consist of lapses of nearly regular spiking interleaved by others of highly irregular one. We explore here the emergence of these structures and show their correspondence to the intermittent transitions to chaos. In fact, the average residence time in the nearly-periodic firing state, obeys the same scaling law -- as a function of the control parameter -- than the one at the onset type I intermittency for dynamical systems in the vicinity of a saddle node bifurcation. We hypothesize that this scenario is also present in a variety of slow-fast neuron models characterized by the coexistence of a two-dimensional fast manifold and a one-dimensional slow one.
