Pyragas Kestutis, Fedaravičius Augustinas P, Pyragienė Tatjana
Department of Fundamental Research, Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania.
Phys Rev E. 2021 Jul;104(1-1):014203. doi: 10.1103/PhysRevE.104.014203.
Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.
在一个由两个相互作用的兴奋性和抑制性二次积分发放神经元群体组成的大规模神经网络中，分析了集体振荡及其通过外部刺激的抑制情况。在神经元数量无限的极限情况下，该网络的微观模型可以简化为一个精确的低维平均场方程组。对这些方程的分岔分析揭示了自由网络中的三种不同动态模式：稳定的静止状态、稳定的极限环以及静止状态和极限环共存的双稳态。我们表明，在极限环模式下，对抑制性群体的高频刺激可以稳定不稳定的静止状态并有效抑制集体振荡。我们还表明，在双稳态模式下，通过对兴奋性群体施加抑制脉冲，可以将网络的动态从稳定的极限环切换到稳定的静止状态。从平均场方程获得的结果通过微观模型的数值模拟得到了证实。
