Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil.
Phys Rev E. 2019 Dec;100(6-1):062416. doi: 10.1103/PhysRevE.100.062416.
We study a model with excitable neurons modeled as stochastic units with three states, representing quiescence, firing, and refractoriness. The transition rates between quiescence and firing depend exponentially on the number of firing neighbors, whereas all other rates are kept constant. This model class was shown to exhibit collective oscillations (synchronization) if neurons are spiking autonomously, but not if neurons are in the excitable regime. In both cases, neurons were restricted to interact through excitatory coupling. Here we show that a plethora of collective phenomena appear if inhibitory coupling is added. Besides the usual transition between an absorbing and an active phase, the model with excitatory and inhibitory neurons can also undergo reentrant transitions to an oscillatory phase. In the mean-field description, oscillations can emerge through supercritical or subcritical Hopf bifurcations, as well as through infinite period bifurcations. The model has bistability between active and oscillating behavior, as well as collective excitability, a regime where the system can display a peak of global activity when subject to a sufficiently strong perturbation. We employ a variant of the Shinomoto-Kuramoto order parameter to characterize the phase transitions and their system-size dependence.
我们研究了一个具有兴奋性神经元的模型，这些神经元被建模为具有三个状态的随机单元，分别表示静息、放电和不应期。从静息状态到放电状态的跃迁速率与放电邻居的数量呈指数关系，而其他所有速率都保持不变。如果神经元自主放电，该模型类被证明会表现出集体振荡（同步），但如果神经元处于兴奋状态则不会。在这两种情况下，神经元都被限制通过兴奋性耦合进行相互作用。在这里，我们表明，如果加入抑制性耦合，会出现大量的集体现象。除了通常在吸收相和活跃相之间的转变之外，具有兴奋性和抑制性神经元的模型还可以经历到振荡相的折返转变。在平均场描述中，振荡可以通过超临界或亚临界 Hopf 分岔，以及通过无限周期分岔出现。该模型在活跃和振荡行为之间具有双稳定性，以及集体兴奋性，即当系统受到足够强的扰动时，系统可以显示全局活动峰值的状态。我们采用 Shinomoto-Kuramoto 序参量的变体来描述相转变及其对系统大小的依赖性。
