Dipartimento di Neuroscienze, Scienze Riproduttive e Odontostomatologiche, Università di Napoli Federico II, Via S. Pansini 5, 80131 Napoli, Italy.
Dipartimento di Fisica "E. Pancini", Università di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, via Cintia, 80126 Napoli, Italy.
Phys Rev E. 2023 Mar;107(3-1):034404. doi: 10.1103/PhysRevE.107.034404.
We study a stochastic version of the Wilson-Cowan model of neural dynamics, where the response function of neurons grows faster than linearly above the threshold. The model shows a region of parameters where two attractive fixed points of the dynamics exist simultaneously. One fixed point is characterized by lower activity and scale-free critical behavior, while the second fixed point corresponds to a higher (supercritical) persistent activity, with small fluctuations around a mean value. When the number of neurons is not too large, the system can switch between these two different states with a probability depending on the parameters of the network. Along with alternation of states, the model displays a bimodal distribution of the avalanches of activity, with a power-law behavior corresponding to the critical state, and a bump of very large avalanches due to the high-activity supercritical state. The bistability is due to the presence of a first-order (discontinuous) transition in the phase diagram, and the observed critical behavior is connected with the line where the low-activity state becomes unstable (spinodal line).
我们研究了神经动力学的威尔逊-考恩模型的随机版本，其中神经元的响应函数在阈值以上呈线性增长。该模型显示了动力学存在两个吸引力固定点的参数区域。一个固定点的特点是活性较低，具有无标度临界行为，而第二个固定点对应于更高的（超临界）持续活性，平均值周围的波动较小。当神经元的数量不是太大时，系统可以根据网络的参数以一定的概率在这两种不同状态之间切换。随着状态的交替，模型显示出活动的雪崩的双峰分布，具有与临界状态对应的幂律行为，以及由于高活性超临界状态而导致的非常大的雪崩的凸起。双稳定性是由于相图中存在一阶（不连续）转变，而观察到的临界行为与低活性状态变得不稳定的线（旋度线）有关。
