标题： 对极低外部波动的敏感性和Greenberg-Hastings神经元模型的临界行为 显示英文标题

标题： Susceptibility for extremely low external fluctuations and critical behaviour of Greenberg-Hastings neuronal model

摘要： 我们考虑与Greenberg-Hastings神经网络模型中平均激活相关的涨落敏感度的标度行为及其与微观自发激活的关系。 我们发现，当自发激活概率趋于零时，敏感度中出现了明显的有限尺寸标度行为，其特征是临界指数遵循已知的标度定律。 这表明，自发激活概率在动力学激活转变中扮演着与序参量共轭的外部场的角色。 该模型在不同动力学相变附近的不同激活机制的作用通过数值方法和平均场近似进行了表征。 显示英文摘要

摘要： We consider the scaling behaviour of the fluctuation susceptibility associated with the average activation in the Greenberg-Hastings neural network model and its relation to microscopic spontaneous activation. We found that, as the spontaneous activation probability tends to zero, a clear finite size scaling behaviour in the susceptibility emerges, characterized by critical exponents which follow already known scaling laws. This shows that the spontaneous activation probability plays the role of an external field conjugated to the order parameter of the dynamical activation transition. The roles of different kinds of activation mechanisms around the different dynamical phase transitions exhibited by the model are characterized numerically and using a mean field approximation.