Max Planck Institute for Mathematics in Sciences, Inselstr.22, Leipzig, 04103, Saxony, Germany.
Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, United States.
J Comput Neurosci. 2023 Feb;51(1):149-172. doi: 10.1007/s10827-022-00838-4. Epub 2022 Oct 25.
We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-fire neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron gain function and a linear Poisson neuron approximation which we use to study mean-field dynamics of the EI population and its bifurcations. In the low firing rate regime, the quiescent state loses stability due to saddle-node or Hopf bifurcations. In particular, at the Bogdanov-Takens (BT) bifurcation point which is the intersection of the Hopf bifurcation and the saddle-node bifurcation lines of the 2D dynamical system, the network shows avalanche dynamics with power-law avalanche size and duration distributions. This matches the characteristics of low firing spontaneous activity in the cortex. By linearizing gain functions and excitatory and inhibitory nullclines, we can approximate the location of the BT bifurcation point. This point in the control parameter phase space corresponds to the internal balance of excitation and inhibition and a slight excess of external excitatory input to the excitatory population. Due to the tight balance of average excitation and inhibition currents, the firing of the individual cells is fluctuation-driven. Around the BT point, the spiking of neurons is a Poisson process and the population average membrane potential of neurons is approximately at the middle of the operating interval [Formula: see text]. Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes.
我们研究了具有基于电导的突触的兴奋和抑制（EI）稀疏连接的放电积分和放电神经元群体的自发临界动力学。我们使用自下而上的方法推导出单个神经元增益函数和线性泊松神经元近似值，我们使用该增益函数和线性泊松神经元近似值来研究 EI 群体及其分岔的平均场动力学。在低发射率区域，由于鞍结或 Hopf 分岔，静止状态失去稳定性。特别是，在 Bogdanov-Takens（BT）分岔点（即 Hopf 分岔与二维动力系统的鞍结分岔线的交点），网络显示具有幂律大小和持续时间分布的雪崩动力学。这与皮质中低发射自发活动的特征相匹配。通过线性化增益函数和兴奋和抑制零轨迹，可以近似 BT 分岔点的位置。该控制参数相空间中的点对应于兴奋和抑制的内部平衡，以及兴奋群体中外部兴奋输入的轻微过剩。由于平均兴奋和抑制电流的紧密平衡，单个细胞的发射是由波动驱动的。在 BT 点周围，神经元的放电是泊松过程，神经元的群体平均膜电位大约在工作间隔[公式：见文本]的中间。此外，EI 网络接近振荡和活跃-不活跃相变两种状态。
